IMO 2010 Shortlist A6

Suppose that f and g are two functions defined on the set of positive integers and taking positive integer values. Suppo...

IMO 2010 Shortlist A6

Category: Algebra

Problem

Suppose that f and g are two functions defined on the set of positive integers and taking positive integer values. Suppose also that the equations fpgpnqq  fpnq 1 and gpfpnqq  gpnq 1 hold for all positive integers. Prove that fpnqgpnq for all positive integer n. (Germany)