2011 AIME II Problems/Problem 14

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Problem:

There are N permutations $(a_{1}, a_{2}, ... , a_{30})$ of 1, 2, ... , 30 such that for $m \in \left\{{2, 3, 5}\right\}$, m divides $a_{n+m} - a_{n}$ for all integers n with $1 \leq n < n+m \leq 30$. Find the remainder when N is divided by 1000.

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