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69th Belarusian Mathematical Olympiad

Belarus number theory

Problem

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.

Final answer

No, such an integer does not exist.

Techniques

Fermat / Euler / Wilson theoremsMultiplicative order