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2013 China Western Mathematical Olympiad ,Problem 8

Source: China Lanzhou 18 Aug 2013

August 18, 2013
inductionmodular arithmeticnumber theory proposednumber theory

Problem Statement

Find all positive integers aa such that for any positive integer n≥5n\ge 5 we have 2n−n2∣an−na2^n-n^2\mid a^n-n^a.
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