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Integer and Integer

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

For how many values of $n$ are both $n$ and $\frac{n+3}{n-1}$ integers?

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.
View the archive of all weekly problems grouped by curriculum topic