MathDB

u^n - v^n are integers for infinite many n

Source: 2016 Saudi Arabia Pre-TST Level 4 2.3

September 13, 2020

number theorypositive integers

Problem Statement

Let

u

and

v

be positive rational numbers with

u \ne v

. Assume that there are infinitely many positive integers

n

with the property that

u^n - v^n

are integers. Prove that

u

and

v

are integers.