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Source: Romania NMO 2021 grade 12

April 25, 2021
number theory

Problem Statement

Given is an positive integer a>2a>2 a) Prove that there exists positive integer nn different from 11, which is not a prime, such that an=1(modn)a^n=1(mod n) b) Prove that if pp is the smallest positive integer, different from 11, such that ap=1(modp)a^p=1(mod p), then pp is a prime. c) There does not exist positive integer nn, different from 11, such that 2n=1(modn)2^n=1(mod n)
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