Permutation Order II
Public  02/08/18  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]
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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