**EGMO 2014, Problem 3**. We denote the number of positive divisors of a positive integer \(m\) by \(d(m)\) and the number of distinct prime divisors of \(m\) by \(\omega(m)\). Let \(k\) be a positive integer. Prove that there exist infinitely many positive integers \(n\) such that \(\omega(n) = k\) and \(d(n)\) does not divide \(d(a^2+b^2)\) for any positive integers \(a, b\) satisfying \(a + b = n\).