Square Product

Weekly Problem 10 - 2011
Will this product give a perfect square?
Exploring and noticing Working systematically Conjecturing and generalising Visualising and representing Reasoning, convincing and proving
Being curious Being resourceful Being resilient Being collaborative

Problem



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.