IMO 2021 Shortlist N5

Prove that there are only finitely many quadruples pa,b,c,nq of positive integers such that n! “an´1 bn´1 cn´1 .

IMO 2021 Shortlist N5

Category: Number Theory

Problem

Prove that there are only finitely many quadruples pa,b,c,nq of positive integers such that n! “an´1 bn´1 cn´1 .