I have been looking through the book Counterexamples: From Elementary Calculus to the Beginning of Calculus and became interested in the section on periodic functions. I thought of the following question: Suppose you have a periodic real valued function f(x) with a fundamental period T. Let c be an integer greater than 1. Is it possible for f(x)+f(cx) to have a fundamental period less than T? Many simple examples would seem to indicate that the answer is no, but I can't find a proof and have failed to develop my own proof. I searched through many other books on counterexamples and can't seem to find an example that would indicate the answer is yes.