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ASU 360 All Soviet Union MO 1983 n^m / m^n and k^n / n^k =>k^m / m^k

Source:

July 28, 2019
number theorydivisibleexponential

Problem Statement

Given natural n,m,kn,m,k. It is known that mnm^n is divisible by nmn^m, and nkn^k is divisible by knk^n. Prove that mkm^k is divisible by kmk^m.
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