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Harmonic Triangle

Can you see how to build a harmonic triangle? Can you work out the next two rows?


Stage: 4 Short Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3
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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.