3

Part of 2012 Finnish National High School Mathematics Competition

Problems(1)

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

Source: Finland 2012, Problem 3

Prove that for all integers

k\geq 2,

k^{k-1}-1

is divisible by

(k-1)^2.

algebrabinomial theoremnumber theory unsolvednumber theory