Here's a math puzzle for you: Suppose f is a function from the natural numbers (1,2,3...) to the natural numbers, and (f(m)+n)(f(n)+m) is a square for all m,n. What functions f have this property? It's easy to guess what f has to be, but the puzzle is to prove that the possibilities for f are limited to your guess - or show what other possibilities there are. If you happen to see the solution onl…