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Interesting divisibility condition on exponential expressions

Source: IMEO 2019, Problem 5

October 14, 2019
number theorynumber theory proposedDivisibility

Problem Statement

Find all pairs of positive integers (s,t)(s, t), so that for any two different positive integers aa and bb there exists some positive integer nn, for which as+bt∣an+bn+1.a^s + b^t | a^n + b^{n+1}.
Proposed by Oleksii Masalitin (Ukraine)
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