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1^{p+2} + 2^{p+2} + ...+(p-1)^{p+2} is divisible by p^2

Source: Balkan MO Shortlist 2013 N4 BMO

March 9, 2020

number theorydivisibleSum of powersdivisor

Problem Statement

Let

p

be a prime number greater than

3

. Prove that the sum

1^{p+2} + 2^{p+2} + ...+ (p-1)^{p+2}

is divisible by

p^2