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Indonesia National Science Olympiad 2010 - Day 1 Problem 4

Source:

September 28, 2010

number theory unsolvednumber theory

Problem Statement

Given that

m

and

n

are positive integers with property:

(mn)\mid(m^{2010}+n^{2010}+n)

Show that there exists a positive integer

k

such that

n=k^{2010}

Nanang Susyanto, Yogyakarta