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Divisibility of a factorial

Source: Own

June 6, 2014
factorialnumber theory proposednumber theory

Problem Statement

pp and qq are distinct prime numbers. Prove that the number (pq−1)!pq−1qp−1(p−1)!(q−1)!\frac {(pq-1)!} {p^{q-1}q^{p-1}(p-1)!(q-1)!} is an integer.
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