IMO 2011 Shortlist A4
Determine all pairs (f,g) of functions from the set of positive integers to itself that satisfy fg(n)+1 (n) + gf(n) (n) ...
Category: Algebra
Problem
Determine all pairs (f,g) of functions from the set of positive integers to itself that satisfy fg(n)+1 (n) + gf(n) (n) = f(n + 1) − g(n + 1) + 1 for every positive integer n. Here, fk (n) means f(f(...f | {z } k (n)...)).