IMO 2019 Shortlist N1

Find all pairs pm,nq of positive integers satisfying the equation p2n ´ 1qp2n ´ 2qp2n ´ 4q¨¨¨p2n ´ 2n´1 q “ m! (El Salva...

imomathematicsolympiadshortlistnumber-theory

IMO 2019 Shortlist N1

Category: Number Theory

Problem

Find all pairs pm,nq of positive integers satisfying the equation p2n ´ 1qp2n ´ 2qp2n ´ 4q¨¨¨p2n ´ 2n´1 q “ m! (El Salvador)