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n^{n-1}-m^{m-1} is not divisible by k

Source: MEMO 2009, problem 4, single competition

October 1, 2009
quadraticsmodular arithmeticnumber theorynumber theory proposed

Problem Statement

Determine all integers k≥2 k\ge 2 such that for all pairs (m (m, n) n) of different positive integers not greater than k k, the number n^{n\minus{}1}\minus{}m^{m\minus{}1} is not divisible by k k.
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