Challenge Level

As $n$ takes each positive integer value in turn (that is, $n=1$, $n=2$, $n=3$...) how many different values are obtained for the remainder when $n^2$ is divided by $n+4$?

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.

This problem is taken from the UKMT Mathematical Challenges.

You can find more short problems, arranged by curriculum topic, in our short problems collection.