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a^i+b^i divisiblity

Source: IMOC 2020

September 4, 2020
IMOCnumber theoryDivisibility

Problem Statement

<spanclass=′latex−bold′>N4:</span><span class='latex-bold'>N4:</span> Let a,ba,b be two positive integers such that for all positive integer n>20202020n>2020^{2020}, there exists a positive integer mm coprime to nn with \begin{align*} \text{ an+bn∣am+bma^n+b^n \mid a^m+b^m} \end{align*} Show that a=ba=b Proposed by ltf0501
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