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Harmonic Triangle

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

Leftovers

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

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.