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Divisibility over a million?

Source: Ukrainian Mathematical Olympiad 2021. Day 1, Problem 9.2

December 21, 2023
number theoryDivisibility

Problem Statement

Prove that there exist distinct positive integers aa and bb greater than 10000001000000 such that (ab+1)(a^b + 1) is divisible by (ba+1)(b^a + 1).
Proposed by Arsenii Nikolaiev
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