Competition problem — Number theory

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Number theory Difficulty 5.0 AIME Prove it Belarus

Does there exist an integer $n > 1$ such that $2^{n-1} + 1$ is divisible by $n$ ?

Solution

See T. Andreescu, G. Dospinescu, Problems from the Book, 2008, P. 54, Ex. 7.

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Source: MathNet, licensed CC-BY-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.