Problem Solving Set 9

12 July 2012

1. Let x, y, and z be integers such that n = x^{4} + y^{4} + z^{4} is divisible by 29. Show that n is divisible by 29^{4}.

2. Find all continuous odd functions f : ℝ → ℝ such that the identity f(f(x)) = x holds for all real x.