Time for another problem of the week! This one doesn’t necessarily require any number-theoretic knowledge, although a little bit might help point you in the right direction. As usual, let be the set of natural numbers, i.e., the set of nonnegative integers.
Describe all functions such that for all .
Please submit solutions to topological[dot]musings[At]gmail[dot]com by Sunday, November 2, 11:59 pm (UTC); do not submit solutions in Comments. Everyone with a correct solution will be inducted into our Hall of Fame! We look forward to your response.