Challenge Level

What is the smallest integer $n$ such that the product $$(2^2 -1)(3^2 -1)(4^2 -1)...(n^2 -1)$$is a perfect square?

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.