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$(k-1)^2$ divides $k^{k-1}-1$

Source: Finland 2012, Problem 3

May 5, 2013
algebrabinomial theoremnumber theory unsolvednumber theory

Problem Statement

Prove that for all integers k≥2,k\geq 2, the number kk−1−1k^{k-1}-1 is divisible by (k−1)2.(k-1)^2.
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