MathDB

4

Part of 2009 Middle European Mathematical Olympiad

Problems(1)

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

Source: MEMO 2009, problem 4, single competition

10/1/2009
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.
quadraticsmodular arithmeticnumber theorynumber theory proposed