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# Pisano period

Pisano period
You are encouraged to solve this task according to the task description, using any language you may know.

The Fibonacci sequence taken modulo 2 is a periodic sequence of period 3 : 0, 1, 1, 0, 1, 1, ...

For any integer n, the Fibonacci sequence taken modulo n is periodic and the length of the periodic cycle is referred to as the Pisano period.

Prime numbers are straightforward; the Pisano period of a prime number p is simply: pisano(p). The Pisano period of a composite number c may be found in different ways. It may be calculated directly: pisano(c), which works, but may be time consuming to find, especially for larger integers, or, it may be calculated by finding the least common multiple of the Pisano periods of each composite component.

E.G.

Given a Pisano period function: pisano(x), and a least common multiple function lcm(x, y):

```   pisano(m × n) is equivalent to lcm(pisano(m), pisano(n)) where  m  and  n  are coprime
```

A formulae to calculate the pisano period for integer powers   k   of prime numbers   p   is:

```   pisano(pk) == p(k-1)pisano(p)
```

The equation is conjectured, no exceptions have been seen.

If a positive integer   i   is split into its prime factors,   then the second and first equations above can be applied to generate the pisano period.

Write 2 functions: pisanoPrime(p,k) and pisano(m).

pisanoPrime(p,k) should return the Pisano period of pk where p is prime and k is a positive integer.

pisano(m) should use pisanoPrime to return the Pisano period of m where m is a positive integer.

Print pisanoPrime(p,2) for every prime lower than 15.

Print pisanoPrime(p,1) for every prime lower than 180.

Print pisano(m) for every integer from 1 to 180.

## Factor

Works with: Factor version 0.99 2020-01-23
`USING: formatting fry grouping io kernel math math.functionsmath.primes math.primes.factors math.ranges sequences ; : pisano-period ( m -- n )    [ 0 1 ] dip [ sq <iota> ] [ ] bi    '[ drop tuck + _ mod 2dup [ zero? ] [ 1 = ] bi* and ]    find 3nip [ 1 + ] [ 1 ] if* ; : pisano-prime ( p k -- n )    over prime? [ "p must be prime." throw ] unless    ^ pisano-period ; : pisano ( m -- n )    group-factors [ first2 pisano-prime ] [ lcm ] map-reduce ; : show-pisano ( upto m -- )    [ primes-upto ] dip    [ 2dup pisano-prime "%d %d pisano-prime = %d\n" printf ]    curry each nl ; 15  2 show-pisano180 1 show-pisano "n pisano for integers 'n' from 2 to 180:" print2 180 [a,b] [ pisano ] map 15 group[ [ "%3d " printf ] each nl ] each`
Output:
```2 2 pisano-prime = 6
3 2 pisano-prime = 24
5 2 pisano-prime = 100
7 2 pisano-prime = 112
11 2 pisano-prime = 110
13 2 pisano-prime = 364

2 1 pisano-prime = 3
3 1 pisano-prime = 8
5 1 pisano-prime = 20
7 1 pisano-prime = 16
11 1 pisano-prime = 10
13 1 pisano-prime = 28
17 1 pisano-prime = 36
19 1 pisano-prime = 18
23 1 pisano-prime = 48
29 1 pisano-prime = 14
31 1 pisano-prime = 30
37 1 pisano-prime = 76
41 1 pisano-prime = 40
43 1 pisano-prime = 88
47 1 pisano-prime = 32
53 1 pisano-prime = 108
59 1 pisano-prime = 58
61 1 pisano-prime = 60
67 1 pisano-prime = 136
71 1 pisano-prime = 70
73 1 pisano-prime = 148
79 1 pisano-prime = 78
83 1 pisano-prime = 168
89 1 pisano-prime = 44
97 1 pisano-prime = 196
101 1 pisano-prime = 50
103 1 pisano-prime = 208
107 1 pisano-prime = 72
109 1 pisano-prime = 108
113 1 pisano-prime = 76
127 1 pisano-prime = 256
131 1 pisano-prime = 130
137 1 pisano-prime = 276
139 1 pisano-prime = 46
149 1 pisano-prime = 148
151 1 pisano-prime = 50
157 1 pisano-prime = 316
163 1 pisano-prime = 328
167 1 pisano-prime = 336
173 1 pisano-prime = 348
179 1 pisano-prime = 178

n pisano for integers 'n' from 2 to 180:
3   8   6  20  24  16  12  24  60  10  24  28  48  40  24
36  24  18  60  16  30  48  24 100  84  72  48  14 120  30
48  40  36  80  24  76  18  56  60  40  48  88  30 120  48
32  24 112 300  72  84 108  72  20  48  72  42  58 120  60
30  48  96 140 120 136  36  48 240  70  24 148 228 200  18
80 168  78 120 216 120 168  48 180 264  56  60  44 120 112
48 120  96 180  48 196 336 120 300  50  72 208  84  80 108
72  72 108  60 152  48  76  72 240  42 168 174 144 120 110
60  40  30 500  48 256 192  88 420 130 120 144 408 360  36
276  48  46 240  32 210 140  24 140 444 112 228 148 600  50
36  72 240  60 168 316  78 216 240  48 216 328 120  40 168
336  48 364 180  72 264 348 168 400 120 232 132 178 120
```

## Go

`package main import "fmt" func gcd(a, b uint) uint {    if b == 0 {        return a    }    return gcd(b, a%b)} func lcm(a, b uint) uint {    return a / gcd(a, b) * b} func ipow(x, p uint) uint {    prod := uint(1)    for p > 0 {        if p&1 != 0 {            prod *= x        }        p >>= 1        x *= x    }    return prod} // Gets the prime decomposition of n.func getPrimes(n uint) []uint {    var primes []uint    for i := uint(2); i <= n; i++ {        div := n / i        mod := n % i        for mod == 0 {            primes = append(primes, i)            n = div            div = n / i            mod = n % i        }    }    return primes} // OK for 'small' numbers.func isPrime(n uint) bool {    switch {    case n < 2:        return false    case n%2 == 0:        return n == 2    case n%3 == 0:        return n == 3    default:        d := uint(5)        for d*d <= n {            if n%d == 0 {                return false            }            d += 2            if n%d == 0 {                return false            }            d += 4        }        return true    }} // Calculates the Pisano period of 'm' from first principles.func pisanoPeriod(m uint) uint {    var p, c uint = 0, 1    for i := uint(0); i < m*m; i++ {        p, c = c, (p+c)%m        if p == 0 && c == 1 {            return i + 1        }    }    return 1} // Calculates the Pisano period of p^k where 'p' is prime and 'k' is a positive integer.func pisanoPrime(p uint, k uint) uint {    if !isPrime(p) || k == 0 {        return 0 // can't do this one    }    return ipow(p, k-1) * pisanoPeriod(p)} // Calculates the Pisano period of 'm' using pisanoPrime.func pisano(m uint) uint {    primes := getPrimes(m)    primePowers := make(map[uint]uint)    for _, p := range primes {        primePowers[p]++    }    var pps []uint    for k, v := range primePowers {        pps = append(pps, pisanoPrime(k, v))    }    if len(pps) == 0 {        return 1    }    if len(pps) == 1 {        return pps[0]    }        f := pps[0]    for i := 1; i < len(pps); i++ {        f = lcm(f, pps[i])    }    return f} func main() {    for p := uint(2); p < 15; p++ {        pp := pisanoPrime(p, 2)        if pp > 0 {            fmt.Printf("pisanoPrime(%2d: 2) = %d\n", p, pp)        }    }    fmt.Println()    for p := uint(2); p < 180; p++ {        pp := pisanoPrime(p, 1)        if pp > 0 {            fmt.Printf("pisanoPrime(%3d: 1) = %d\n", p, pp)        }    }    fmt.Println()    fmt.Println("pisano(n) for integers 'n' from 1 to 180 are:")    for n := uint(1); n <= 180; n++ {        fmt.Printf("%3d ", pisano(n))        if n != 1 && n%15 == 0 {            fmt.Println()        }    }        fmt.Println()}`
Output:
```pisanoPrime( 2: 2) = 6
pisanoPrime( 3: 2) = 24
pisanoPrime( 5: 2) = 100
pisanoPrime( 7: 2) = 112
pisanoPrime(11: 2) = 110
pisanoPrime(13: 2) = 364

pisanoPrime(  2: 1) = 3
pisanoPrime(  3: 1) = 8
pisanoPrime(  5: 1) = 20
pisanoPrime(  7: 1) = 16
pisanoPrime( 11: 1) = 10
pisanoPrime( 13: 1) = 28
pisanoPrime( 17: 1) = 36
pisanoPrime( 19: 1) = 18
pisanoPrime( 23: 1) = 48
pisanoPrime( 29: 1) = 14
pisanoPrime( 31: 1) = 30
pisanoPrime( 37: 1) = 76
pisanoPrime( 41: 1) = 40
pisanoPrime( 43: 1) = 88
pisanoPrime( 47: 1) = 32
pisanoPrime( 53: 1) = 108
pisanoPrime( 59: 1) = 58
pisanoPrime( 61: 1) = 60
pisanoPrime( 67: 1) = 136
pisanoPrime( 71: 1) = 70
pisanoPrime( 73: 1) = 148
pisanoPrime( 79: 1) = 78
pisanoPrime( 83: 1) = 168
pisanoPrime( 89: 1) = 44
pisanoPrime( 97: 1) = 196
pisanoPrime(101: 1) = 50
pisanoPrime(103: 1) = 208
pisanoPrime(107: 1) = 72
pisanoPrime(109: 1) = 108
pisanoPrime(113: 1) = 76
pisanoPrime(127: 1) = 256
pisanoPrime(131: 1) = 130
pisanoPrime(137: 1) = 276
pisanoPrime(139: 1) = 46
pisanoPrime(149: 1) = 148
pisanoPrime(151: 1) = 50
pisanoPrime(157: 1) = 316
pisanoPrime(163: 1) = 328
pisanoPrime(167: 1) = 336
pisanoPrime(173: 1) = 348
pisanoPrime(179: 1) = 178

pisano(n) for integers 'n' from 1 to 180 are:
1   3   8   6  20  24  16  12  24  60  10  24  28  48  40
24  36  24  18  60  16  30  48  24 100  84  72  48  14 120
30  48  40  36  80  24  76  18  56  60  40  48  88  30 120
48  32  24 112 300  72  84 108  72  20  48  72  42  58 120
60  30  48  96 140 120 136  36  48 240  70  24 148 228 200
18  80 168  78 120 216 120 168  48 180 264  56  60  44 120
112  48 120  96 180  48 196 336 120 300  50  72 208  84  80
108  72  72 108  60 152  48  76  72 240  42 168 174 144 120
110  60  40  30 500  48 256 192  88 420 130 120 144 408 360
36 276  48  46 240  32 210 140  24 140 444 112 228 148 600
50  36  72 240  60 168 316  78 216 240  48 216 328 120  40
168 336  48 364 180  72 264 348 168 400 120 232 132 178 120
```

`import qualified Data.Text as T main = do  putStrLn "PisanoPrime(p,2) for prime p lower than 15"  putStrLn . see 15 . map (`pisanoPrime` 2) . filter isPrime \$ [1 .. 15]  putStrLn "PisanoPrime(p,1) for prime p lower than 180"  putStrLn . see 15 . map (`pisanoPrime` 1) . filter isPrime \$ [1 .. 180]  let ns = [1 .. 180] :: [Int]  let xs = map pisanoPeriod ns  let ys = map pisano ns  let zs = map pisanoConjecture ns  putStrLn "Pisano(m) for m from 1 to 180"  putStrLn . see 15 \$ map pisano [1 .. 180]  putStrLn \$    "map pisanoPeriod [1..180] == map pisano [1..180] = " ++ show (xs == ys)  putStrLn \$    "map pisanoPeriod [1..180] == map pisanoConjecture [1..180] = " ++    show (ys == zs) bagOf :: Int -> [a] -> [[a]]bagOf _ [] = []bagOf n xs =  let (us, vs) = splitAt n xs  in us : bagOf n vs see  :: Show a  => Int -> [a] -> Stringsee n =  unlines .  map unwords . bagOf n . map (T.unpack . T.justifyRight 3 ' ' . T.pack . show) fibMod  :: Integral a  => a -> [a]fibMod 1 = repeat 0fibMod n = fib  where    fib = 0 : 1 : zipWith (\x y -> rem (x + y) n) fib (tail fib) pisanoPeriod  :: Integral a  => a -> apisanoPeriod m  | m <= 0 = 0pisanoPeriod 1 = 1pisanoPeriod m = go 1 (tail \$ fibMod m)  where    go t (0:1:_) = t    go t (_:xs) = go (succ t) xs powMod  :: Integral a  => a -> a -> a -> apowMod _ _ k  | k < 0 = error "negative power"powMod m _ _  | 1 == abs m = 0powMod m p k  | 1 == abs p = mod v m  where    v      | 1 == p || even k = 1      | otherwise = ppowMod m p k = go p k  where    to x y = mod (x * y) m    go _ 0 = 1    go u 1 = mod u m    go u i      | even i = to w w      | otherwise = to u (to w w)      where        w = go u (quot i 2) -- Fermat primality testprobablyPrime  :: Integral a  => a -> BoolprobablyPrime p  | p < 2 || even p = 2 == p  | otherwise = 1 == powMod p 2 (p - 1) primes  :: Integral a  => [a]primes =  2 :  3 :  5 :  7 :  [ p  | p <- [11,13 ..]   , isPrime p ] limitDivisor  :: Integral a  => a -> alimitDivisor = floor . (+ 0.05) . sqrt . fromIntegral isPrime  :: Integral a  => a -> BoolisPrime p  | not \$ probablyPrime p = FalseisPrime p = go primes  where    stop = limitDivisor p    go (n:_)      | stop < n = True    go (n:ns) = (0 /= rem p n) && go ns    go [] = True factor  :: Integral a  => a -> [(a, a)]factor n  | n <= 1 = []factor n = go n primes  where    fun x d c      | 0 /= rem x d = (x, c)      | otherwise = fun (quot x d) d (succ c)    go 1 _ = []    go _ [] = []    go x (d:ds)      | 0 /= rem x d = go x \$ dropWhile ((0 /=) . rem x) ds    go x (d:ds) =      let (u, c) = fun (quot x d) d 1      in (d, c) : go u ds pisanoPrime  :: Integral a  => a -> a -> apisanoPrime p k  | p <= 0 || k < 0 = 0pisanoPrime p k = pisanoPeriod \$ p ^ k pisano  :: Integral a  => a -> apisano m  | m < 1 = 0pisano 1 = 1pisano m = foldl1 lcm . map (uncurry pisanoPrime) \$ factor m pisanoConjecture  :: Integral a  => a -> apisanoConjecture m  | m < 1 = 0pisanoConjecture 1 = 1pisanoConjecture m = foldl1 lcm . map (uncurry pisanoPrime') \$ factor m  where    pisanoPrime' p k = (p ^ (k - 1)) * pisanoPeriod p`
Output:
```PisanoPrime(p,2) for prime p lower than 15
6  24 100 112 110 364

PisanoPrime(p,1) for prime p lower than 180
3   8  20  16  10  28  36  18  48  14  30  76  40  88  32
108  58  60 136  70 148  78 168  44 196  50 208  72 108  76
256 130 276  46 148  50 316 328 336 348 178

Pisano(m) for m from 1 to 180
1   3   8   6  20  24  16  12  24  60  10  24  28  48  40
24  36  24  18  60  16  30  48  24 100  84  72  48  14 120
30  48  40  36  80  24  76  18  56  60  40  48  88  30 120
48  32  24 112 300  72  84 108  72  20  48  72  42  58 120
60  30  48  96 140 120 136  36  48 240  70  24 148 228 200
18  80 168  78 120 216 120 168  48 180 264  56  60  44 120
112  48 120  96 180  48 196 336 120 300  50  72 208  84  80
108  72  72 108  60 152  48  76  72 240  42 168 174 144 120
110  60  40  30 500  48 256 192  88 420 130 120 144 408 360
36 276  48  46 240  32 210 140  24 140 444 112 228 148 600
50  36  72 240  60 168 316  78 216 240  48 216 328 120  40
168 336  48 364 180  72 264 348 168 400 120 232 132 178 120

map pisanoPeriod [1..180] == map pisano [1..180] = True
map pisanoPeriod [1..180] == map pisanoConjecture [1..180] = True```

## Java

Use efficient algorithm to calculate period.

` import java.util.ArrayList;import java.util.Collections;import java.util.HashMap;import java.util.List;import java.util.Map;import java.util.TreeMap; public class PisanoPeriod {     public static void main(String[] args) {        System.out.printf("Print pisano(p^2) for every prime p lower than 15%n");        for ( long i = 2 ; i < 15 ; i++ ) {             if ( isPrime(i) ) {                long n = i*i;                 System.out.printf("pisano(%d) = %d%n", n, pisano(n));            }        }         System.out.printf("%nPrint pisano(p) for every prime p lower than 180%n");        for ( long n = 2 ; n < 180 ; n++ ) {             if ( isPrime(n) ) {                 System.out.printf("pisano(%d) = %d%n", n, pisano(n));            }        }         System.out.printf("%nPrint pisano(n) for every integer from 1 to 180%n");        for ( long n = 1 ; n <= 180 ; n++ ) {             System.out.printf("%3d  ", pisano(n));            if ( n % 10 == 0 ) {                System.out.printf("%n");            }        }      }     private static final boolean isPrime(long test) {        if ( test == 2 ) {            return true;        }        if ( test % 2 == 0 ) {            return false;        }        for ( long i = 3 ; i <= Math.sqrt(test) ; i += 2 ) {            if ( test % i == 0 ) {                return false;            }        }        return true;    }      private static Map<Long,Long> PERIOD_MEMO = new HashMap<>();    static {        PERIOD_MEMO.put(2L, 3L);        PERIOD_MEMO.put(3L, 8L);        PERIOD_MEMO.put(5L, 20L);            }     //  See http://webspace.ship.edu/msrenault/fibonacci/fib.htm    private static long pisano(long n) {        if ( PERIOD_MEMO.containsKey(n) ) {            return PERIOD_MEMO.get(n);        }        if ( n == 1 ) {            return 1;        }        Map<Long,Long> factors = getFactors(n);         //  Special cases        //  pisano(2^k) = 3*n/2        if ( factors.size() == 1 & factors.get(2L) != null && factors.get(2L) > 0 ) {            long result = 3 * n / 2;            PERIOD_MEMO.put(n, result);            return result;        }        //  pisano(5^k) = 4*n        if ( factors.size() == 1 & factors.get(5L) != null && factors.get(5L) > 0 ) {            long result = 4*n;            PERIOD_MEMO.put(n, result);            return result;        }        //  pisano(2*5^k) = 6*n        if ( factors.size() == 2 & factors.get(2L) != null && factors.get(2L) == 1 && factors.get(5L) != null && factors.get(5L) > 0 ) {            long result = 6*n;            PERIOD_MEMO.put(n, result);            return result;        }         List<Long> primes = new ArrayList<>(factors.keySet());        long prime = primes.get(0);        if ( factors.size() == 1 && factors.get(prime) == 1 ) {            List<Long> divisors = new ArrayList<>();            if ( n % 10 == 1 || n % 10 == 9 ) {                for ( long divisor : getDivisors(prime-1) ) {                    if ( divisor % 2 == 0 ) {                        divisors.add(divisor);                    }                }            }            else {                List<Long> pPlus1Divisors = getDivisors(prime+1);                for ( long divisor : getDivisors(2*prime+2) ) {                    if ( !  pPlus1Divisors.contains(divisor) ) {                        divisors.add(divisor);                    }                }            }            Collections.sort(divisors);            for ( long divisor : divisors ) {                if ( fibModIdentity(divisor, prime) ) {                    PERIOD_MEMO.put(prime, divisor);                    return divisor;                }            }            throw new RuntimeException("ERROR 144: Divisor not found.");        }        long period = (long) Math.pow(prime, factors.get(prime)-1) * pisano(prime);        for ( int i = 1 ; i < primes.size() ; i++ ) {            prime = primes.get(i);            period = lcm(period, (long) Math.pow(prime, factors.get(prime)-1) * pisano(prime));        }        PERIOD_MEMO.put(n, period);        return period;    }     //  Use Matrix multiplication to compute Fibonacci numbers.    private static boolean fibModIdentity(long n, long mod) {        long aRes = 0;        long bRes = 1;        long cRes = 1;        long aBase = 0;        long bBase = 1;        long cBase = 1;        while ( n > 0 ) {            if ( n % 2 == 1 ) {                long temp1 = 0, temp2 = 0, temp3 = 0;                if ( aRes > SQRT || aBase > SQRT || bRes > SQRT || bBase > SQRT || cBase > SQRT || cRes > SQRT ) {                    temp1 = (multiply(aRes, aBase, mod) + multiply(bRes, bBase, mod)) % mod;                    temp2 = (multiply(aBase, bRes, mod) + multiply(bBase, cRes, mod)) % mod;                    temp3 = (multiply(bBase, bRes, mod) + multiply(cBase, cRes, mod)) % mod;                }                else {                    temp1 = ((aRes*aBase % mod) + (bRes*bBase % mod)) % mod;                    temp2 = ((aBase*bRes % mod) + (bBase*cRes % mod)) % mod;                    temp3 = ((bBase*bRes % mod) + (cBase*cRes % mod)) % mod;                }                aRes = temp1;                bRes = temp2;                cRes = temp3;            }            n >>= 1L;            long temp1 = 0, temp2 = 0, temp3 = 0;             if ( aBase > SQRT || bBase > SQRT || cBase > SQRT ) {                temp1 = (multiply(aBase, aBase, mod) + multiply(bBase, bBase, mod)) % mod;                temp2 = (multiply(aBase, bBase, mod) + multiply(bBase, cBase, mod)) % mod;                temp3 = (multiply(bBase, bBase, mod) + multiply(cBase, cBase, mod)) % mod;            }            else {                temp1 = ((aBase*aBase % mod) + (bBase*bBase % mod)) % mod;                temp2 = ((aBase*bBase % mod) + (bBase*cBase % mod)) % mod;                temp3 = ((bBase*bBase % mod) + (cBase*cBase % mod)) % mod;            }            aBase = temp1;            bBase = temp2;            cBase = temp3;        }        return aRes % mod == 0 && bRes % mod == 1 && cRes % mod == 1;    }     private static final long SQRT = (long) Math.sqrt(Long.MAX_VALUE);     //  Result is a*b % mod, without overflow.    public static final long multiply(long a, long b, long modulus) {        //System.out.println("    multiply : a = " + a + ", b = " + b + ", mod = " + modulus);        long x = 0;        long y = a % modulus;        long t;        while ( b > 0 ) {            if ( b % 2 == 1 ) {                t = x + y;                x = (t > modulus ? t-modulus : t);            }            t = y << 1;            y = (t > modulus ? t-modulus : t);            b >>= 1;        }        //System.out.println("    multiply : answer = " + (x % modulus));        return x % modulus;    }     private static final List<Long> getDivisors(long number) {        List<Long> divisors = new ArrayList<>();        long sqrt = (long) Math.sqrt(number);        for ( long i = 1 ; i <= sqrt ; i++ ) {            if ( number % i == 0 ) {                divisors.add(i);                long div = number / i;                if ( div != i ) {                    divisors.add(div);                }            }        }        return divisors;    }     public static long lcm(long a, long b) {        return a*b/gcd(a,b);    }     public static long gcd(long a, long b) {        if ( b == 0 ) {            return a;        }        return gcd(b, a%b);    }     private static final Map<Long,Map<Long,Long>> allFactors = new TreeMap<Long,Map<Long,Long>>();    static {        Map<Long,Long> factors = new TreeMap<Long,Long>();        factors.put(2L, 1L);        allFactors.put(2L, factors);    }     public static Long MAX_ALL_FACTORS = 100000L;     public static final Map<Long,Long> getFactors(Long number) {        if ( allFactors.containsKey(number) ) {            return allFactors.get(number);        }        Map<Long,Long> factors = new TreeMap<Long,Long>();        if ( number % 2 == 0 ) {            Map<Long,Long> factorsdDivTwo = getFactors(number/2);            factors.putAll(factorsdDivTwo);            factors.merge(2L, 1L, (v1, v2) -> v1 + v2);            if ( number < MAX_ALL_FACTORS ) {                allFactors.put(number, factors);            }            return factors;        }        boolean prime = true;        long sqrt = (long) Math.sqrt(number);        for ( long i = 3 ; i <= sqrt ; i += 2 ) {            if ( number % i == 0 ) {                prime = false;                factors.putAll(getFactors(number/i));                factors.merge(i, 1L, (v1, v2) -> v1 + v2);                if ( number < MAX_ALL_FACTORS ) {                    allFactors.put(number, factors);                }                return factors;            }        }        if ( prime ) {            factors.put(number, 1L);            if ( number < MAX_ALL_FACTORS ) {                 allFactors.put(number, factors);            }        }        return factors;    } } `
Output:
```Print pisano(p^2) for every prime p lower than 15
pisano(4) = 6
pisano(9) = 24
pisano(25) = 100
pisano(49) = 112
pisano(121) = 110
pisano(169) = 364

Print pisano(p) for every prime p lower than 180
pisano(2) = 3
pisano(3) = 8
pisano(5) = 20
pisano(7) = 16
pisano(11) = 10
pisano(13) = 28
pisano(17) = 36
pisano(19) = 18
pisano(23) = 48
pisano(29) = 14
pisano(31) = 30
pisano(37) = 76
pisano(41) = 40
pisano(43) = 88
pisano(47) = 32
pisano(53) = 108
pisano(59) = 58
pisano(61) = 60
pisano(67) = 136
pisano(71) = 70
pisano(73) = 148
pisano(79) = 78
pisano(83) = 168
pisano(89) = 44
pisano(97) = 196
pisano(101) = 50
pisano(103) = 208
pisano(107) = 72
pisano(109) = 108
pisano(113) = 76
pisano(127) = 256
pisano(131) = 130
pisano(137) = 276
pisano(139) = 46
pisano(149) = 148
pisano(151) = 50
pisano(157) = 316
pisano(163) = 328
pisano(167) = 336
pisano(173) = 348
pisano(179) = 178

Print pisano(n) for every integer from 1 to 180
1    3    8    6   20   24   16   12   24   60
10   24   28   48   40   24   36   24   18   60
16   30   48   24  100   84   72   48   14  120
30   48   40   36   80   24   76   18   56   60
40   48   88   30  120   48   32   24  112  300
72   84  108   72   20   48   72   42   58  120
60   30   48   96  140  120  136   36   48  240
70   24  148  228  200   18   80  168   78  120
216  120  168   48  180  264   56   60   44  120
112   48  120   96  180   48  196  336  120  300
50   72  208   84   80  108   72   72  108   60
152   48   76   72  240   42  168  174  144  120
110   60   40   30  500   48  256  192   88  420
130  120  144  408  360   36  276   48   46  240
32  210  140   24  140  444  112  228  148  600
50   36   72  240   60  168  316   78  216  240
48  216  328  120   40  168  336   48  364  180
72  264  348  168  400  120  232  132  178  120
```

## Julia

`using Primes const pisanos = Dict{Int, Int}()function pisano(p)    p < 2 && return 1    (i = get(pisanos, p, 0)) > 0 && return i    lastn, n = 0, 1    for i in 1:p^2        lastn, n = n, (lastn + n) % p        if lastn == 0 && n == 1            pisanos[p] = i            return i        end    end    return 1end pisanoprime(p, k) = (@assert(isprime(p)); p^(k-1) * pisano(p))pisanotask(n) = mapreduce(p -> pisanoprime(p[1], p[2]), lcm, collect(factor(n)), init=1) for i in 1:15    if isprime(i)        println("pisanoPrime(\$i, 2) = ", pisanoprime(i, 2))    endend for i in 1:180    if isprime(i)        println("pisanoPrime(\$i, 1) = ", pisanoprime(i, 1))    endend println("\nPisano(n) for n from 2 to 180:\n", [pisano(i) for i in 2:180])println("\nPisano(n) using pisanoPrime for n from 2 to 180:\n", [pisanotask(i) for i in 2:180]) `
Output:
```pisanoPrime(2, 2) = 6
pisanoPrime(3, 2) = 24
pisanoPrime(5, 2) = 100
pisanoPrime(7, 2) = 112
pisanoPrime(11, 2) = 110
pisanoPrime(13, 2) = 364
pisanoPrime(2, 1) = 3
pisanoPrime(3, 1) = 8
pisanoPrime(5, 1) = 20
pisanoPrime(7, 1) = 16
pisanoPrime(11, 1) = 10
pisanoPrime(13, 1) = 28
pisanoPrime(17, 1) = 36
pisanoPrime(19, 1) = 18
pisanoPrime(23, 1) = 48
pisanoPrime(29, 1) = 14
pisanoPrime(31, 1) = 30
pisanoPrime(37, 1) = 76
pisanoPrime(41, 1) = 40
pisanoPrime(43, 1) = 88
pisanoPrime(47, 1) = 32
pisanoPrime(53, 1) = 108
pisanoPrime(59, 1) = 58
pisanoPrime(61, 1) = 60
pisanoPrime(67, 1) = 136
pisanoPrime(71, 1) = 70
pisanoPrime(73, 1) = 148
pisanoPrime(79, 1) = 78
pisanoPrime(83, 1) = 168
pisanoPrime(89, 1) = 44
pisanoPrime(97, 1) = 196
pisanoPrime(101, 1) = 50
pisanoPrime(103, 1) = 208
pisanoPrime(107, 1) = 72
pisanoPrime(109, 1) = 108
pisanoPrime(113, 1) = 76
pisanoPrime(127, 1) = 256
pisanoPrime(131, 1) = 130
pisanoPrime(137, 1) = 276
pisanoPrime(139, 1) = 46
pisanoPrime(149, 1) = 148
pisanoPrime(151, 1) = 50
pisanoPrime(157, 1) = 316
pisanoPrime(163, 1) = 328
pisanoPrime(167, 1) = 336
pisanoPrime(173, 1) = 348
pisanoPrime(179, 1) = 178

Pisano(n) for n from 2 to 180:
[3, 8, 6, 20, 24, 16, 12, 24, 60, 10, 24, 28, 48, 40, 24, 36, 24, 18, 60, 16, 30, 48, 24, 100, 84, 72, 48, 14, 120, 30, 48, 40, 36, 80, 24, 76, 18, 56, 60, 40, 48, 88, 30, 120, 48, 32, 24, 112, 300, 72, 84, 108, 72, 20, 48, 72, 42, 58, 120, 60, 30, 48, 96, 140, 120, 136, 36, 48, 240, 70, 24, 148, 228, 200, 18, 80, 168, 78, 120, 216, 120, 168, 48, 180, 264, 56, 60, 44, 120, 112, 48, 120, 96, 180, 48, 196, 336, 120, 300, 50, 72, 208, 84, 80, 108, 72, 72, 108, 60, 152, 48, 76, 72, 240, 42, 168, 174, 144, 120, 110, 60, 40, 30, 500, 48, 256, 192, 88, 420, 130, 120, 144, 408, 360, 36, 276, 48, 46, 240, 32, 210, 140, 24, 140, 444, 112, 228, 148, 600, 50, 36, 72, 240, 60, 168, 316, 78, 216, 240, 48, 216, 328, 120, 40, 168, 336, 48, 364, 180, 72, 264, 348, 168, 400, 120, 232, 132, 178, 120]

Pisano(n) using pisanoPrime for n from 2 to 180:
[3, 8, 6, 20, 24, 16, 12, 24, 60, 10, 24, 28, 48, 40, 24, 36, 24, 18, 60, 16, 30, 48, 24, 100, 84, 72, 48, 14, 120, 30, 48, 40, 36, 80, 24, 76, 18, 56, 60, 40, 48, 88, 30, 120, 48, 32, 24, 112, 300, 72, 84, 108, 72, 20, 48, 72, 42, 58, 120, 60, 30, 48, 96, 140, 120, 136, 36, 48, 240, 70, 24, 148, 228, 200, 18, 80, 168, 78, 120, 216, 120, 168, 48, 180, 264, 56, 60, 44, 120, 112, 48, 120, 96, 180, 48, 196, 336, 120, 300, 50, 72, 208, 84, 80, 108, 72, 72, 108, 60, 152, 48, 76, 72, 240, 42, 168, 174, 144, 120, 110, 60, 40, 30, 500, 48, 256, 192, 88, 420, 130, 120, 144, 408, 360, 36, 276, 48, 46, 240, 32, 210, 140, 24, 140, 444, 112, 228, 148, 600, 50, 36, 72, 240, 60, 168, 316, 78, 216, 240, 48, 216, 328, 120, 40, 168, 336, 48, 364, 180, 72, 264, 348, 168, 400, 120, 232, 132, 178, 120]
```

## Nim

Translation of: Go
`import math, strformat, tables func primes(n: Positive): seq[int] =  ## Return the list of prime divisors of "n".  var n = n.int  for d in 2..n:    var q = n div d    var m = n mod d    while m == 0:      result.add d      n = q      q = n div d      m = n mod d func isPrime(n: Positive): bool =  ## Return true if "n" is prime.  if n < 2: return false  if n mod 2 == 0: return n == 2  if n mod 3 == 0: return n == 3  var d = 5  while d <= sqrt(n.toFloat).int:    if n mod d == 0: return false    inc d, 2    if n mod d == 0: return false    inc d, 4  result = true func pisanoPeriod(m: Positive): int =  ## Calculate the Pisano period of 'm' from first principles.  var p = 0  var c = 1  for i in 0..<m*m:    p = (p + c) mod m    swap p, c    if p == 0 and c == 1: return i + 1  result = 1 func pisanoPrime(p, k: Positive): int =  ## Calculate the Pisano period of p^k where 'p' is prime and 'k' is a positive integer.  if p.isPrime: p^(k-1) * p.pisanoPeriod() else: 0 func pisano(m: Positive): int =  ## Calculate the Pisano period of 'm' using pisanoPrime.  let primes = m.primes  var primePowers = primes.toCountTable  var pps: seq[int]  for k, v in primePowers.pairs:    pps.add pisanoPrime(k, v)  if pps.len == 0: return 1  result = pps[0]  for i in 1..pps.high:    result = lcm(result, pps[i])  when isMainModule:   for p in 2..14:    let pp = pisanoPrime(p, 2)    if pp > 0:      echo &"pisanoPrime({p:2}, 2) = {pp}"   echo()  for p in 2..179:    let pp = pisanoPrime(p, 1)    if pp > 0:      echo &"pisanoPrime({p:3}, 1) = {pp}"   echo()  echo "pisano(n) for integers 'n' from 1 to 180 are:"  for n in 1..180:    stdout.write &"{pisano(n):3}", if n mod 15 == 0: '\n' else: ' '`
Output:
```pisanoPrime( 2, 2) = 6
pisanoPrime( 3, 2) = 24
pisanoPrime( 5, 2) = 100
pisanoPrime( 7, 2) = 112
pisanoPrime(11, 2) = 110
pisanoPrime(13, 2) = 364

pisanoPrime(  2, 1) = 3
pisanoPrime(  3, 1) = 8
pisanoPrime(  5, 1) = 20
pisanoPrime(  7, 1) = 16
pisanoPrime( 11, 1) = 10
pisanoPrime( 13, 1) = 28
pisanoPrime( 17, 1) = 36
pisanoPrime( 19, 1) = 18
pisanoPrime( 23, 1) = 48
pisanoPrime( 29, 1) = 14
pisanoPrime( 31, 1) = 30
pisanoPrime( 37, 1) = 76
pisanoPrime( 41, 1) = 40
pisanoPrime( 43, 1) = 88
pisanoPrime( 47, 1) = 32
pisanoPrime( 53, 1) = 108
pisanoPrime( 59, 1) = 58
pisanoPrime( 61, 1) = 60
pisanoPrime( 67, 1) = 136
pisanoPrime( 71, 1) = 70
pisanoPrime( 73, 1) = 148
pisanoPrime( 79, 1) = 78
pisanoPrime( 83, 1) = 168
pisanoPrime( 89, 1) = 44
pisanoPrime( 97, 1) = 196
pisanoPrime(101, 1) = 50
pisanoPrime(103, 1) = 208
pisanoPrime(107, 1) = 72
pisanoPrime(109, 1) = 108
pisanoPrime(113, 1) = 76
pisanoPrime(127, 1) = 256
pisanoPrime(131, 1) = 130
pisanoPrime(137, 1) = 276
pisanoPrime(139, 1) = 46
pisanoPrime(149, 1) = 148
pisanoPrime(151, 1) = 50
pisanoPrime(157, 1) = 316
pisanoPrime(163, 1) = 328
pisanoPrime(167, 1) = 336
pisanoPrime(173, 1) = 348
pisanoPrime(179, 1) = 178

pisano(n) for integers 'n' from 1 to 180 are:
1   3   8   6  20  24  16  12  24  60  10  24  28  48  40
24  36  24  18  60  16  30  48  24 100  84  72  48  14 120
30  48  40  36  80  24  76  18  56  60  40  48  88  30 120
48  32  24 112 300  72  84 108  72  20  48  72  42  58 120
60  30  48  96 140 120 136  36  48 240  70  24 148 228 200
18  80 168  78 120 216 120 168  48 180 264  56  60  44 120
112  48 120  96 180  48 196 336 120 300  50  72 208  84  80
108  72  72 108  60 152  48  76  72 240  42 168 174 144 120
110  60  40  30 500  48 256 192  88 420 130 120 144 408 360
36 276  48  46 240  32 210 140  24 140 444 112 228 148 600
50  36  72 240  60 168 316  78 216 240  48 216 328 120  40
168 336  48 364 180  72 264 348 168 400 120 232 132 178 120```

## Perl

Translation of: Sidef
Library: ntheory
`use strict;use warnings;use feature 'say';use ntheory qw(primes factor_exp lcm); sub pisano_period_pp {    my(\$a, \$b, \$n, \$k) = (0, 1, \$_[0]**\$_[1]);    while (++\$k) {        (\$a, \$b) = (\$b, (\$a+\$b) % \$n);        return \$k if \$a == 0 and \$b == 1;    }} sub pisano_period {    (lcm map { pisano_period_pp(\$\$_[0],\$\$_[1]) } factor_exp(\$_[0])) or 1;} sub display { (sprintf "@{['%5d' x @_]}", @_) =~ s/(.{75})/\$1\n/gr } say "Pisano periods for squares of primes p <= 50:\n", display( map { pisano_period_pp(\$_, 2) } @{primes(1,  50)} ),  "\nPisano periods for primes p <= 180:\n",           display( map { pisano_period_pp(\$_, 1) } @{primes(1, 180)} ),"\n\nPisano periods for integers n from 1 to 180:\n",  display( map { pisano_period   (\$_   ) }          1..180   );`
Output:
```Pisano periods for squares of primes p <= 50:
6   24  100  112  110  364  612  342 1104  406  930 2812 1640 3784 1504

Pisano periods for primes p <= 180:
3    8   20   16   10   28   36   18   48   14   30   76   40   88   32
108   58   60  136   70  148   78  168   44  196   50  208   72  108   76
256  130  276   46  148   50  316  328  336  348  178

Pisano periods for integers n from 1 to 180:
1    3    8    6   20   24   16   12   24   60   10   24   28   48   40
24   36   24   18   60   16   30   48   24  100   84   72   48   14  120
30   48   40   36   80   24   76   18   56   60   40   48   88   30  120
48   32   24  112  300   72   84  108   72   20   48   72   42   58  120
60   30   48   96  140  120  136   36   48  240   70   24  148  228  200
18   80  168   78  120  216  120  168   48  180  264   56   60   44  120
112   48  120   96  180   48  196  336  120  300   50   72  208   84   80
108   72   72  108   60  152   48   76   72  240   42  168  174  144  120
110   60   40   30  500   48  256  192   88  420  130  120  144  408  360
36  276   48   46  240   32  210  140   24  140  444  112  228  148  600
50   36   72  240   60  168  316   78  216  240   48  216  328  120   40
168  336   48  364  180   72  264  348  168  400  120  232  132  178  120```

## Phix

`function pisano_period(integer m)-- Calculates the Pisano period of 'm' from first principles. (copied from Go)    integer p = 0, c = 1    for i=0 to m*m-1 do        {p, c} = {c, mod(p+c,m)}        if p == 0 and c == 1 then            return i + 1        end if    end for    return 1end function function pisanoPrime(integer p, k)    if not is_prime(p) or k=0 then ?9/0 end if    return power(p,k-1)*pisano_period(p)end function function pisano(integer m)-- Calculates the Pisano period of 'm' using pisanoPrime.    if m=1 then return 1 end if    sequence s = prime_factors(m, true, get_maxprime(m))&0,             pps = {}    integer k = 1, p = s[1]    for i=2 to length(s) do        integer n = s[i]        if n!=p then            pps = append(pps,pisanoPrime(p,k))            {k,p} = {1,n}        else            k += 1        end if    end for    return lcm(pps)end function procedure p(integer k, lim)-- test harness    printf(1,"pisanoPrimes")    integer pdx = 1, c = 0    while true do        integer p = get_prime(pdx)        if p>=lim then exit end if        c += 1        if c=7 then puts(1,"\n            ") c = 1        elsif pdx>1 then puts(1,", ") end if        printf(1,"(%3d,%d)=%3d",{p,k,pisanoPrime(p,k)})        pdx += 1    end while    printf(1,"\n")end procedurep(2,15)p(1,180) sequence p180 = {}for n=1 to 180 do p180 &= pisano(n) end forprintf(1,"pisano(1..180):\n")pp(p180,{pp_IntFmt,"%4d",pp_IntCh,false})`
Output:
```pisanoPrimes(  2,2)=  6, (  3,2)= 24, (  5,2)=100, (  7,2)=112, ( 11,2)=110, ( 13,2)=364
pisanoPrimes(  2,1)=  3, (  3,1)=  8, (  5,1)= 20, (  7,1)= 16, ( 11,1)= 10, ( 13,1)= 28
( 17,1)= 36, ( 19,1)= 18, ( 23,1)= 48, ( 29,1)= 14, ( 31,1)= 30, ( 37,1)= 76
( 41,1)= 40, ( 43,1)= 88, ( 47,1)= 32, ( 53,1)=108, ( 59,1)= 58, ( 61,1)= 60
( 67,1)=136, ( 71,1)= 70, ( 73,1)=148, ( 79,1)= 78, ( 83,1)=168, ( 89,1)= 44
( 97,1)=196, (101,1)= 50, (103,1)=208, (107,1)= 72, (109,1)=108, (113,1)= 76
(127,1)=256, (131,1)=130, (137,1)=276, (139,1)= 46, (149,1)=148, (151,1)= 50
(157,1)=316, (163,1)=328, (167,1)=336, (173,1)=348, (179,1)=178
pisano(1..180):
{   1,   3,   8,   6,  20,  24,  16,  12,  24,  60,  10,  24,  28,  48,  40,
24,  36,  24,  18,  60,  16,  30,  48,  24, 100,  84,  72,  48,  14, 120,
30,  48,  40,  36,  80,  24,  76,  18,  56,  60,  40,  48,  88,  30, 120,
48,  32,  24, 112, 300,  72,  84, 108,  72,  20,  48,  72,  42,  58, 120,
60,  30,  48,  96, 140, 120, 136,  36,  48, 240,  70,  24, 148, 228, 200,
18,  80, 168,  78, 120, 216, 120, 168,  48, 180, 264,  56,  60,  44, 120,
112,  48, 120,  96, 180,  48, 196, 336, 120, 300,  50,  72, 208,  84,  80,
108,  72,  72, 108,  60, 152,  48,  76,  72, 240,  42, 168, 174, 144, 120,
110,  60,  40,  30, 500,  48, 256, 192,  88, 420, 130, 120, 144, 408, 360,
36, 276,  48,  46, 240,  32, 210, 140,  24, 140, 444, 112, 228, 148, 600,
50,  36,  72, 240,  60, 168, 316,  78, 216, 240,  48, 216, 328, 120,  40,
168, 336,  48, 364, 180,  72, 264, 348, 168, 400, 120, 232, 132, 178, 120}
```

## Python

Uses the SymPy library.

`from sympy import isprime, lcm, factorint, primerangefrom functools import reduce  def pisano1(m):    "Simple definition"    if m < 2:        return 1    lastn, n = 0, 1    for i in range(m ** 2):        lastn, n = n, (lastn + n) % m        if lastn == 0 and n == 1:            return i + 1    return 1 def pisanoprime(p, k):    "Use conjecture π(p ** k) == p ** (k − 1) * π(p) for prime p and int k > 1"    assert isprime(p) and k > 0    return p ** (k - 1) * pisano1(p) def pisano_mult(m, n):    "pisano(m*n) where m and n assumed coprime integers"    return lcm(pisano1(m), pisano1(n)) def pisano2(m):    "Uses prime factorization of m"    return reduce(lcm, (pisanoprime(prime, mult)                        for prime, mult in factorint(m).items()), 1)  if __name__ == '__main__':    for n in range(1, 181):        assert pisano1(n) == pisano2(n), "Wall-Sun-Sun prime exists??!!"    print("\nPisano period (p, 2) for primes less than 50\n ",          [pisanoprime(prime, 2) for prime in primerange(1, 50)])    print("\nPisano period (p, 1) for primes less than 180\n ",          [pisanoprime(prime, 1) for prime in primerange(1, 180)])    print("\nPisano period (p) for integers 1 to 180")    for i in range(1, 181):        print(" %3d" % pisano2(i), end="" if i % 10 else "\n")`
Output:
```Pisano period (p, 2) for primes less than 50
[6, 24, 100, 112, 110, 364, 612, 342, 1104, 406, 930, 2812, 1640, 3784, 1504]

Pisano period (p, 1) for primes less than 180
[3, 8, 20, 16, 10, 28, 36, 18, 48, 14, 30, 76, 40, 88, 32, 108, 58, 60, 136, 70, 148, 78, 168, 44, 196, 50, 208, 72, 108, 76, 256, 130, 276, 46, 148, 50, 316, 328, 336, 348, 178]

Pisano period (p) for integers 1 to 180
1   3   8   6  20  24  16  12  24  60
10  24  28  48  40  24  36  24  18  60
16  30  48  24 100  84  72  48  14 120
30  48  40  36  80  24  76  18  56  60
40  48  88  30 120  48  32  24 112 300
72  84 108  72  20  48  72  42  58 120
60  30  48  96 140 120 136  36  48 240
70  24 148 228 200  18  80 168  78 120
216 120 168  48 180 264  56  60  44 120
112  48 120  96 180  48 196 336 120 300
50  72 208  84  80 108  72  72 108  60
152  48  76  72 240  42 168 174 144 120
110  60  40  30 500  48 256 192  88 420
130 120 144 408 360  36 276  48  46 240
32 210 140  24 140 444 112 228 148 600
50  36  72 240  60 168 316  78 216 240
48 216 328 120  40 168 336  48 364 180
72 264 348 168 400 120 232 132 178 120```

## Raku

(formerly Perl 6)

Works with: Rakudo version 2020.02

Didn't bother making two differently named routines, just made a multi that will auto dispatch to the correct candidate.

`use Prime::Factor; constant @fib := 1,1,*+*…*; my %cache; multi pisano-period (Int \$p where *.is-prime, Int \$k where * > 0 = 1) {    return %cache{"\$p|\$k"} if %cache{"\$p|\$k"};    my \$fibmod = @fib.map: * % \$p**\$k;    %cache{"\$p|\$k"} = (1..*).first: { !\$fibmod[\$_-1] and (\$fibmod[\$_] == 1) }} multi pisano-period (Int \$p where * > 0 ) {    [lcm] prime-factors(\$p).Bag.map: { samewith .key, .value }}  put "Pisano period (p, 2) for primes less than 50";put (map { pisano-period(\$_, 2) }, ^50 .grep: *.is-prime )».fmt('%4d'); put "\nPisano period (p, 1) for primes less than 180";.put for (map { pisano-period(\$_, 1) }, ^180 .grep: *.is-prime )».fmt('%4d').batch(15); put "\nPisano period (p, 1) for integers 1 to 180";.put for (1..180).map( { pisano-period(\$_) } )».fmt('%4d').batch(15);`
Output:
```Pisano period (p, 2) for primes less than 50
6   24  100  112  110  364  612  342 1104  406  930 2812 1640 3784 1504

Pisano period (p, 1) for primes less than 180
3    8   20   16   10   28   36   18   48   14   30   76   40   88   32
108   58   60  136   70  148   78  168   44  196   50  208   72  108   76
256  130  276   46  148   50  316  328  336  348  178

Pisano period (p, 1) for integers 1 to 180
1    3    8    6   20   24   16   12   24   60   10   24   28   48   40
24   36   24   18   60   16   30   48   24  100   84   72   48   14  120
30   48   40   36   80   24   76   18   56   60   40   48   88   30  120
48   32   24  112  300   72   84  108   72   20   48   72   42   58  120
60   30   48   96  140  120  136   36   48  240   70   24  148  228  200
18   80  168   78  120  216  120  168   48  180  264   56   60   44  120
112   48  120   96  180   48  196  336  120  300   50   72  208   84   80
108   72   72  108   60  152   48   76   72  240   42  168  174  144  120
110   60   40   30  500   48  256  192   88  420  130  120  144  408  360
36  276   48   46  240   32  210  140   24  140  444  112  228  148  600
50   36   72  240   60  168  316   78  216  240   48  216  328  120   40
168  336   48  364  180   72  264  348  168  400  120  232  132  178  120```

## REXX

`/*REXX pgm calculates pisano period for a range of N, and pisanoPrime(N,m)  [for primes]*/numeric digits 500                               /*ensure enough decimal digits for Fib.*/parse arg lim.1 lim.2 lim.3 .                    /*obtain optional arguments from the CL*/if lim.1=='' | lim.1==","  then lim.1=  15 - 1   /*Not specified?  Then use the default.*/if lim.2=='' | lim.2==","  then lim.2= 180 - 1   /* "      "         "   "   "     "    */if lim.3=='' | lim.3==","  then lim.3= 180       /* "      "         "   "   "     "    */call Fib                                         /*    "      "   Fibonacci numbers.    */         do i=1  for max(lim.1, lim.2, lim.3);  call pisano(i)    /*find pisano periods.*/         end   /*i*/;    w= length(i)     do j=1  for 2;  #= word(2 1, j)       do p=1  for lim.j;  if \isPrime(p)  then iterate  /*Not prime?  Skip this number.*/       say '   pisanoPrime('right(p, w)", "#') = 'right( pisanoPrime(p, #), 5)       end   /*p*/;        say    end      /*j*/ say center(' pisano numbers for 1──►'lim.3" ",  20*4 - 1,  "═")       /*display a title.*/\$=    do j=1  for lim.3;     \$= \$  right(@.j, w)   /*append pisano number to the  \$  list.*/    if j//20==0  then do;  say substr(\$, 2);  \$=;  end    /*display 20 numbers to a line*/    end   /*j*/                           say substr(\$, 2)      /*possible display any residuals──►term*/exit 0                                           /*stick a fork in it,  we're all done. *//*──────────────────────────────────────────────────────────────────────────────────────*/fib: procedure expose fib.; parse arg x; fib.=.;     if x==''      then x= 1000     fib.0= 0;  fib.1= 1;                            if fib.x\==.  then return fib.x                  do k=2  for x-1;    a= k-1;        b= k-2;       fib.k=  fib.a + fib.b                  end   /*k*/;    return fib.k/*──────────────────────────────────────────────────────────────────────────────────────*/isPrime: parse arg n; if n<11  then return pos(n, '2 3 5 7')>0;  if n//2==0  then return 0            do k=3  by 2  while k*k<=n; if n//k==0  then return 0; end /*k*/;     return 1/*──────────────────────────────────────────────────────────────────────────────────────*/pisano: procedure expose @. fib.; parse arg m;   if m==1  then do;  @.m=1;  return 1;  end                do k=1;  _= k+1;                 if fib.k//m==0 & fib._//m==1  then leave                end   /*k*/;      @.m= k;                 return k/*──────────────────────────────────────────────────────────────────────────────────────*/pisanoPrime: procedure expose @. fib.; parse arg m,n;     return m**(n-1)  *  pisano(m)`
output   when using the default inputs:

(Shown at   3/4   size.)

```   pisanoPrime(  2, 2) =     6
pisanoPrime(  3, 2) =    24
pisanoPrime(  5, 2) =   100
pisanoPrime(  7, 2) =   112
pisanoPrime( 11, 2) =   110
pisanoPrime( 13, 2) =   364

pisanoPrime(  2, 1) =     3
pisanoPrime(  3, 1) =     8
pisanoPrime(  5, 1) =    20
pisanoPrime(  7, 1) =    16
pisanoPrime( 11, 1) =    10
pisanoPrime( 13, 1) =    28
pisanoPrime( 17, 1) =    36
pisanoPrime( 19, 1) =    18
pisanoPrime( 23, 1) =    48
pisanoPrime( 29, 1) =    14
pisanoPrime( 31, 1) =    30
pisanoPrime( 37, 1) =    76
pisanoPrime( 41, 1) =    40
pisanoPrime( 43, 1) =    88
pisanoPrime( 47, 1) =    32
pisanoPrime( 53, 1) =   108
pisanoPrime( 59, 1) =    58
pisanoPrime( 61, 1) =    60
pisanoPrime( 67, 1) =   136
pisanoPrime( 71, 1) =    70
pisanoPrime( 73, 1) =   148
pisanoPrime( 79, 1) =    78
pisanoPrime( 83, 1) =   168
pisanoPrime( 89, 1) =    44
pisanoPrime( 97, 1) =   196
pisanoPrime(101, 1) =    50
pisanoPrime(103, 1) =   208
pisanoPrime(107, 1) =    72
pisanoPrime(109, 1) =   108
pisanoPrime(113, 1) =    76
pisanoPrime(127, 1) =   256
pisanoPrime(131, 1) =   130
pisanoPrime(137, 1) =   276
pisanoPrime(139, 1) =    46
pisanoPrime(149, 1) =   148
pisanoPrime(151, 1) =    50
pisanoPrime(157, 1) =   316
pisanoPrime(163, 1) =   328
pisanoPrime(167, 1) =   336
pisanoPrime(173, 1) =   348
pisanoPrime(179, 1) =   178

═════════════════════════ pisano numbers for 1──►180 ══════════════════════════
1   3   8   6  20  24  16  12  24  60  10  24  28  48  40  24  36  24  18  60
16  30  48  24 100  84  72  48  14 120  30  48  40  36  80  24  76  18  56  60
40  48  88  30 120  48  32  24 112 300  72  84 108  72  20  48  72  42  58 120
60  30  48  96 140 120 136  36  48 240  70  24 148 228 200  18  80 168  78 120
216 120 168  48 180 264  56  60  44 120 112  48 120  96 180  48 196 336 120 300
50  72 208  84  80 108  72  72 108  60 152  48  76  72 240  42 168 174 144 120
110  60  40  30 500  48 256 192  88 420 130 120 144 408 360  36 276  48  46 240
32 210 140  24 140 444 112 228 148 600  50  36  72 240  60 168 316  78 216 240
48 216 328 120  40 168 336  48 364 180  72 264 348 168 400 120 232 132 178 120
```

## Sidef

`func pisano_period_pp(p,k) is cached {     assert(k.is_pos,   "k = #{k} must be positive")    assert(p.is_prime, "p = #{p} must be prime")     var (a, b, n) = (0, 1, p**k)     1..Inf -> first_by {        (a, b) = (b, (a+b) % n)        (a == 0) && (b == 1)    }} func pisano_period(n) {    n.factor_map {|p,k| pisano_period_pp(p, k) }.lcm} say "Pisano periods for squares of primes p <= 15:"say  15.primes.map {|p| pisano_period_pp(p, 2) } say "\nPisano periods for primes p <= 180:"say 180.primes.map {|p| pisano_period_pp(p, 1) } say "\nPisano periods for integers n from 1 to 180:"say pisano_period.map(1..180)`
Output:
```Pisano periods for squares of primes p <= 15:
[6, 24, 100, 112, 110, 364]

Pisano periods for primes p <= 180:
[3, 8, 20, 16, 10, 28, 36, 18, 48, 14, 30, 76, 40, 88, 32, 108, 58, 60, 136, 70, 148, 78, 168, 44, 196, 50, 208, 72, 108, 76, 256, 130, 276, 46, 148, 50, 316, 328, 336, 348, 178]

Pisano periods for integers n from 1 to 180:
[1, 3, 8, 6, 20, 24, 16, 12, 24, 60, 10, 24, 28, 48, 40, 24, 36, 24, 18, 60, 16, 30, 48, 24, 100, 84, 72, 48, 14, 120, 30, 48, 40, 36, 80, 24, 76, 18, 56, 60, 40, 48, 88, 30, 120, 48, 32, 24, 112, 300, 72, 84, 108, 72, 20, 48, 72, 42, 58, 120, 60, 30, 48, 96, 140, 120, 136, 36, 48, 240, 70, 24, 148, 228, 200, 18, 80, 168, 78, 120, 216, 120, 168, 48, 180, 264, 56, 60, 44, 120, 112, 48, 120, 96, 180, 48, 196, 336, 120, 300, 50, 72, 208, 84, 80, 108, 72, 72, 108, 60, 152, 48, 76, 72, 240, 42, 168, 174, 144, 120, 110, 60, 40, 30, 500, 48, 256, 192, 88, 420, 130, 120, 144, 408, 360, 36, 276, 48, 46, 240, 32, 210, 140, 24, 140, 444, 112, 228, 148, 600, 50, 36, 72, 240, 60, 168, 316, 78, 216, 240, 48, 216, 328, 120, 40, 168, 336, 48, 364, 180, 72, 264, 348, 168, 400, 120, 232, 132, 178, 120]
```

By assuming that Wall-Sun-Sun primes do not exist, we can compute the Pisano period more efficiently, as illustrated below on Fermat numbers F_n = 2^(2^n) + 1:

`func pisano_period_pp(p, k=1) {    (p - kronecker(5, p)).divisors.first_by {|d| fibmod(d, p) == 0 } * p**(k-1)} func pisano_period(n) {     return 0 if (n <= 0)    return 1 if (n == 1)     var d = n.factor_map {|p,k| pisano_period_pp(p, k) }.lcm     3.times {|k|        var t = d<<k        if ((fibmod(t, n) == 0) && (fibmod(t+1, n) == 1)) {            return t        }    }} for k in (1..8) {    say ("Pisano(F_#{k}) = ", pisano_period(2**(2**k) + 1))}`
Output:
```Pisano(F_1) = 20
Pisano(F_2) = 36
Pisano(F_3) = 516
Pisano(F_4) = 14564
Pisano(F_5) = 2144133760
Pisano(F_6) = 4611702838532647040
Pisano(F_7) = 28356863910078205764000346543980814080
Pisano(F_8) = 3859736307910542962840356678888855900560939475751238269689837480239178278912
```

## Wren

Translation of: Go
Library: Wren-math
Library: Wren-fmt
`import "/math" for Intimport "/fmt" for Fmt // Calculates the Pisano period of 'm' from first principles.var pisanoPeriod = Fn.new { |m|    var p = 0    var c = 1    for (i in 0...m*m) {        var t = p        p = c        c = (t + c) % m        if (p == 0 && c == 1) return i + 1    }    return 1} // Calculates the Pisano period of p^k where 'p' is prime and 'k' is a positive integer.var pisanoPrime = Fn.new { |p, k|    if (!Int.isPrime(p) || k == 0) return 0 // can't do this one    return p.pow(k-1) * pisanoPeriod.call(p)} // Calculates the Pisano period of 'm' using pisanoPrime.var pisano = Fn.new { |m|    var primes = Int.primeFactors(m)    var primePowers = {}    for (p in primes) {        var v = primePowers[p]        primePowers[p] = v ? v + 1 : 1    }    var pps = []    for (me in primePowers) pps.add(pisanoPrime.call(me.key, me.value))    if (pps.count == 0) return 1    if (pps.count == 1) return pps[0]    var f = pps[0]    var i = 1    while (i < pps.count) {        f = Int.lcm(f, pps[i])        i =  i + 1    }    return f} for (p in 2..14) {    var pp = pisanoPrime.call(p, 2)    if (pp > 0) Fmt.print("pisanoPrime(\$2d: 2) = \$d", p, pp)}System.print()for (p in 2..179) {    var pp = pisanoPrime.call(p, 1)    if (pp > 0) Fmt.print("pisanoPrime(\$3d: 1) = \$d", p, pp)}System.print("\npisano(n) for integers 'n' from 1 to 180 are:")for (n in 1..180) {    Fmt.write("\$3d ", pisano.call(n))    if (n != 1 && n%15 == 0) System.print()}System.print()`
Output:
```pisanoPrime( 2: 2) = 6
pisanoPrime( 3: 2) = 24
pisanoPrime( 5: 2) = 100
pisanoPrime( 7: 2) = 112
pisanoPrime(11: 2) = 110
pisanoPrime(13: 2) = 364

pisanoPrime(  2: 1) = 3
pisanoPrime(  3: 1) = 8
pisanoPrime(  5: 1) = 20
pisanoPrime(  7: 1) = 16
pisanoPrime( 11: 1) = 10
pisanoPrime( 13: 1) = 28
pisanoPrime( 17: 1) = 36
pisanoPrime( 19: 1) = 18
pisanoPrime( 23: 1) = 48
pisanoPrime( 29: 1) = 14
pisanoPrime( 31: 1) = 30
pisanoPrime( 37: 1) = 76
pisanoPrime( 41: 1) = 40
pisanoPrime( 43: 1) = 88
pisanoPrime( 47: 1) = 32
pisanoPrime( 53: 1) = 108
pisanoPrime( 59: 1) = 58
pisanoPrime( 61: 1) = 60
pisanoPrime( 67: 1) = 136
pisanoPrime( 71: 1) = 70
pisanoPrime( 73: 1) = 148
pisanoPrime( 79: 1) = 78
pisanoPrime( 83: 1) = 168
pisanoPrime( 89: 1) = 44
pisanoPrime( 97: 1) = 196
pisanoPrime(101: 1) = 50
pisanoPrime(103: 1) = 208
pisanoPrime(107: 1) = 72
pisanoPrime(109: 1) = 108
pisanoPrime(113: 1) = 76
pisanoPrime(127: 1) = 256
pisanoPrime(131: 1) = 130
pisanoPrime(137: 1) = 276
pisanoPrime(139: 1) = 46
pisanoPrime(149: 1) = 148
pisanoPrime(151: 1) = 50
pisanoPrime(157: 1) = 316
pisanoPrime(163: 1) = 328
pisanoPrime(167: 1) = 336
pisanoPrime(173: 1) = 348
pisanoPrime(179: 1) = 178

pisano(n) for integers 'n' from 1 to 180 are:
1   3   8   6  20  24  16  12  24  60  10  24  28  48  40
24  36  24  18  60  16  30  48  24 100  84  72  48  14 120
30  48  40  36  80  24  76  18  56  60  40  48  88  30 120
48  32  24 112 300  72  84 108  72  20  48  72  42  58 120
60  30  48  96 140 120 136  36  48 240  70  24 148 228 200
18  80 168  78 120 216 120 168  48 180 264  56  60  44 120
112  48 120  96 180  48 196 336 120 300  50  72 208  84  80
108  72  72 108  60 152  48  76  72 240  42 168 174 144 120
110  60  40  30 500  48 256 192  88 420 130 120 144 408 360
36 276  48  46 240  32 210 140  24 140 444 112 228 148 600
50  36  72 240  60 168 316  78 216 240  48 216 328 120  40
168 336  48 364 180  72 264 348 168 400 120 232 132 178 120
```

## zkl

Library: GMP
GNU Multiple Precision Arithmetic Library for prime testing
`var [const] BI=Import("zklBigNum");  // libGMP fcn pisanoPeriod(p){   if(p<2) return(0);   lastn,n,t := 0,1,0;   foreach i in ([0..p*p]){      t,n,lastn = n, (lastn + n) % p, t;      if(lastn==0 and n==1) return(i + 1);   }   1}fcn pisanoPrime(p,k){   _assert_(BI(p).probablyPrime(), "%s is not a prime number".fmt(p));   pisanoPeriod(p.pow(k))}`
`println("Pisano period (p, 2) for primes less than 50:");[1..50].pump(List,BI,"probablyPrime",Void.Filter, pisanoPrime.fp1(2))   .concat(" ","   ").println(); println("Pisano period (p, 1) for primes less than 180:");[1..180].pump(List,BI,"probablyPrime",Void.Filter, pisanoPrime.fp1(1))  .pump(Void,T(Void.Read,14,False),fcn{ vm.arglist.apply("%4d".fmt).concat().println() });`
Output:
```Pisano period (p, 2) for primes less than 50:
6 24 100 112 110 364 612 342 1104 406 930 2812 1640 3784 1504
Pisano period (p, 1) for primes less than 180:
3   8  20  16  10  28  36  18  48  14  30  76  40  88  32
108  58  60 136  70 148  78 168  44 196  50 208  72 108  76
256 130 276  46 148  50 316 328 336 348 178
```
`fcn pisano(m){   primeFactors(m).pump(Dictionary().incV)  //18 --> (2,3,3) --> ("2":1, "3":2)     .reduce(fcn(z,[(k,v])){ lcm(z,pisanoPrime(k.toInt(),v)) },1)} fcn lcm(a,b){ a / a.gcd(b) * b }fcn primeFactors(n){  // Return a list of prime factors of n   acc:=fcn(n,k,acc,maxD){  // k is 2,3,5,7,9,... not optimum      if(n==1 or k>maxD) acc.close();      else{	 q,r:=n.divr(k);   // divr-->(quotient,remainder)	 if(r==0) return(self.fcn(q,k,acc.write(k),q.toFloat().sqrt()));	 return(self.fcn(n,k+1+k.isOdd,acc,maxD))  # both are tail recursion      }   }(n,2,Sink(List),n.toFloat().sqrt());   m:=acc.reduce('*,1);      // mulitply factors   if(n!=m) acc.append(n/m); // opps, missed last factor   else acc;}`
`println("Pisano(m) for integers 1 to 180:");[1..180].pump(List, pisano, "%4d".fmt)  .pump(Void,T(Void.Read,14,False),fcn{ vm.arglist.concat().println() });`
Output:
```Pisano(m) for integers 1 to 180:
1   3   8   6  20  24  16  12  24  60  10  24  28  48  40
24  36  24  18  60  16  30  48  24 100  84  72  48  14 120
30  48  40  36  80  24  76  18  56  60  40  48  88  30 120
48  32  24 112 300  72  84 108  72  20  48  72  42  58 120
60  30  48  96 140 120 136  36  48 240  70  24 148 228 200
18  80 168  78 120 216 120 168  48 180 264  56  60  44 120
112  48 120  96 180  48 196 336 120 300  50  72 208  84  80
108  72  72 108  60 152  48  76  72 240  42 168 174 144 120
110  60  40  30 500  48 256 192  88 420 130 120 144 408 360
36 276  48  46 240  32 210 140  24 140 444 112 228 148 600
50  36  72 240  60 168 316  78 216 240  48 216 328 120  40
168 336  48 364 180  72 264 348 168 400 120 232 132 178 120

```