RoseCode

Problem #468

Permutation Order II
 Public ★(x8) 02/08/18 by Philippe_57721 7xp Programming 88.9%

See Problem 467 - Permutation Order I for definitions.

Let $\mathfrak{A}(n,p)$ be the number of permutations of [1..n] with order p

We have:
$\mathfrak{A}(7, 1) = 1$
$\mathfrak{A}(7, 2) = 231$
$\mathfrak{A}(7, 3) = 350$
$\mathfrak{A}(7, 4) = 840$
$\mathfrak{A}(7, 5) = 504$
$\mathfrak{A}(7, 6) = 1470$
$\mathfrak{A}(7, 7) = 720$
$\mathfrak{A}(7,10) = 504$
$\mathfrak{A}(7,12) = 420$

Find the last 10 significant (before trailing 0s) digits of $\mathfrak{A}(1000, 641)$

[My timing: < 100 ms]

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