Let $A$ be a set of $n$ positive integers. Show that every sequence of $2^n$ numbers taken from $A$ contains a consecutive block of numbers whose product is square.(For instance, {2,5,3,2,5,2,3,5} contains the block 5,3,2,5,2,3 .)
I think this has something to do with the pigeon-hole principle but apart from that I have no idea how to proceed any further.
Any hint guys?
Thank You