IMO 2009 Shortlist N7

Let a and b be distinct integers greater than 1. Prove that there exists a positive integer n such that (an − 1)(bn − 1)...

imomathematicsolympiadshortlistnumber-theory

IMO 2009 Shortlist N7

Category: Number Theory

Problem

Let a and b be distinct integers greater than 1. Prove that there exists a positive integer n such that (an − 1)(bn − 1) is not a perfect square.