MathDB

Divisible problem

Source: Vietnam NMO 1985 Problem 4

February 12, 2009

number theory unsolvednumber theory

Problem Statement

Let

a

b

and

m

be positive integers. Prove that there exists a positive integer

n

such that (a^n \minus{} 1)b is divisible by

m

if and only if \gcd (ab, m) \equal{} \gcd (b, m).