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Problem 899

AIME late

Number theory Difficulty 5.7 Prove it

The 90th question: Prove that for any given positive integers $m, n$ , there exist infinitely many pairs of coprime positive integers $a, b$ such that $(a+b) \mid (a m^{a} + b n^{b})$ .

This one wants a proof. Work it on paper, read the official solution, then mark yourself honestly — the ladder only means something if the record is true.

Official solution

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None

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.