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Divisibility by $n!$

Source: Romania TST 1 2010, Problem 5

August 25, 2012
floor functionnumber theorynumber theory proposed

Problem Statement

Let aa and nn be two positive integer numbers such that the (positive) prime factors of aa be all greater than nn. Prove that n!n! divides (a−1)(a2−1)⋯(an−1−1)(a - 1)(a^2 - 1)\cdots (a^{n-1} - 1).
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