Pythagorean triples: Difference between revisions

=={{header|Nanoquery}}==

===Brute force method===

{{trans|Java}}

<lang Nanoquery>import math

// a function to check if three numbers are a valid triple

def is_triple(a, b, c)

if not (a < b) and (b < c)

return false

end

return (a^2 + b^2) = c^2

end

// a function to check if the numbers are coprime

def is_coprime(a, b, c)

global math

return (math.gcd(a, b)=1) && (math.gcd(a, c)=1) && (math.gcd(b, c)=1)

end

// the maximum perimeter to check

perimeter = 100

perimeter2 = int(perimeter / 2) - 1

perimeter3 = int(perimeter / 3) - 1

// loop though and look for pythagorean triples

ts = 0

ps = 0

for a in range(1, perimeter3)

for b in range(a + 1, perimeter2)

for c in range(b + 1, perimeter2)

if (a + b + c) <= perimeter

if is_triple(a,b,c)

ts += 1

print a + ", " + b + ", " + c

if is_coprime(a,b,c)

ps += 1

print " primitive"

end

println

end

end

end

end

end

print "Up to a perimeter of " + perimeter + ", there are " + ts

println " triples, of which " + ps + " are primitive."</lang>

{{out}}

<pre>3, 4, 5 primitive

5, 12, 13 primitive

6, 8, 10

7, 24, 25 primitive

8, 15, 17 primitive

9, 12, 15

9, 40, 41 primitive

10, 24, 26

12, 16, 20

12, 35, 37 primitive

15, 20, 25

15, 36, 39

16, 30, 34

18, 24, 30

20, 21, 29 primitive

21, 28, 35

24, 32, 40

Up to a perimeter of 100, there are 17 triples, of which 7 are primitive.</pre>