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...
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)