IMO 2016 Shortlist N4

Let n,m,k and l be positive integers with n 6= 1 such that nk +mnl +1 divides nk+l −1. Prove that • m = 1 and l = 2k; or...

imomathematicsolympiadshortlistnumber-theory

IMO 2016 Shortlist N4

Category: Number Theory

Problem

Let n,m,k and l be positive integers with n 6= 1 such that nk +mnl +1 divides nk+l −1. Prove that • m = 1 and l = 2k; or • l|k and m = nk−l−1 nl−1 .