Zsigmondy numbers: Difference between revisions

=={{header|Julia}}==

<syntaxhighlight lang="julia">""" Rosetta code task: rosettacode.org/wiki/Zsigmondy_numbers """

using Primes

function divisors(n)

f = [one(n)]

for (p,e) in factor(n)

f = reduce(vcat, [f*p^j for j in 1:e], init=f)

end

return length(f) == 1 ? [one(n), n] : sort!(f)

end

function Zs(n, a, b)

@assert a > b

dexpms = map(i -> a^i - b^i, 1:n-1)

dexpn = a^n - b^n

return maximum(reduce(vcat, filter(d -> all(k -> gcd(k, d) == 1, dexpms), divisors(dexpn))))

end

abs = [(2, 1), (3, 1), (4, 1), (5, 1), (6, 1), (7, 1), (3, 2), (5, 3), (7, 3), (7, 5)]

for (a, b) in abs

println("\nZsigmondy(n, $a, $b): ", join([Zs(n, a, b) for n in 1:20], ", "))

end

</syntaxhighlight>{{out}}

<pre>

Zsigmondy(n, 2, 1): 1, 3, 7, 5, 31, 1, 127, 17, 73, 11, 2047, 13, 8191, 43, 151, 257, 131071, 19, 524287, 41

Zsigmondy(n, 3, 1): 2, 1, 13, 5, 121, 7, 1093, 41, 757, 61, 88573, 73, 797161, 547, 4561, 3281, 64570081, 703, 581130733, 1181

Zsigmondy(n, 4, 1): 3, 5, 7, 17, 341, 13, 5461, 257, 1387, 41, 1398101, 241, 22369621, 3277, 49981, 65537, 5726623061, 4033, 91625968981, 61681

Zsigmondy(n, 5, 1): 4, 3, 31, 13, 781, 7, 19531, 313, 15751, 521, 12207031, 601, 305175781, 13021, 315121, 195313, 190734863281, 5167, 4768371582031, 375601

Zsigmondy(n, 6, 1): 5, 7, 43, 37, 311, 31, 55987, 1297, 46873, 1111, 72559411, 1261, 2612138803, 5713, 1406371, 1679617, 3385331888947, 46441, 121871948002099, 1634221

Zsigmondy(n, 7, 1): 6, 1, 19, 25, 2801, 43, 137257, 1201, 39331, 2101, 329554457, 2353, 16148168401, 102943, 4956001, 2882401, 38771752331201, 117307, 1899815864228857, 1129901

Zsigmondy(n, 3, 2): 1, 5, 19, 13, 211, 7, 2059, 97, 1009, 11, 175099, 61, 1586131, 463, 3571, 6817, 129009091, 577, 1161737179, 4621

Zsigmondy(n, 5, 3): 2, 1, 49, 17, 1441, 19, 37969, 353, 19729, 421, 24325489, 481, 609554401, 10039, 216001, 198593, 381405156481, 12979, 9536162033329, 288961

Zsigmondy(n, 7, 3): 4, 5, 79, 29, 4141, 37, 205339, 1241, 127639, 341, 494287399, 2041, 24221854021, 82573, 3628081, 2885681, 58157596211761, 109117, 2849723505777919, 4871281

Zsigmondy(n, 7, 5): 2, 3, 109, 37, 6841, 13, 372709, 1513, 176149, 1661, 964249309, 1801, 47834153641, 75139, 3162961, 3077713, 115933787267041, 30133, 5689910849522509, 3949201

</pre>