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Interesting number theory

Source: Serbian Mathematical Olympiad 2021, P1

May 14, 2021

number theorySerbia

Problem Statement

Let

a>1

and

c

be natural numbers and let

b\neq 0

be an integer. Prove that there exists a natural number

n

such that the number

a^n+b

has a divisor of the form

cx+1

x\in\mathbb{N}