MathDB

m|a^(n-1)-b^(n-1) and n|a^(m-1)-b^(m-1), infinitude of solns.

Source: Mongolia MO 2001 Grade 10 P3

April 12, 2021

number theoryDivisibility

Problem Statement

Let

a,b

be coprime positive integers with

a

even and

a>b

. Show that there exist infinitely many pairs

(m,n)

of coprime positive integers such that

m\mid a^{n-1}-b^{n-1}

and

n\mid a^{m-1}-b^{m-1}