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If k-n divides k^m - n^(m-1), prove that k <= 2n-1

Source: INAMO 2003 - Problem 7

August 5, 2011
number theory unsolvednumber theory

Problem Statement

Let k,m,nk,m,n be positive integers such that k>n>1k > n > 1 and (k,n)=1(k,n) = 1. If k−n∣km−nm−1k-n | k^m - n^{m-1}, prove that k≤2n−1k \le 2n - 1.
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