Prove that there are infinitely many positive integers n such n(n+1) can b expressed as a sum of two positive squares in at least two different ways.(a^2 + b^2 and b^2 + a^2 are considered as the same representation.....
So the question is. "Are there infinite many such having this property?". The answer is yes. This is a consequence of the Pellian equation is you really want to show it.