Times Square

Prove that the product of four consecutive positive integers cannot be a perfect square.

	Select Click for Answer
If n is the smallest of the four integers, then the product is (n)(n+1)(n+2)(n+3) = (n² + 3n)(n² + 3n + 2) = (n² + 3n + 1)² – 1 This can’t be a perfect square, because two positive squares cannot differ by 1. From Angela Dunn’s Mathematical Bafflers, via David Wells’ Penguin Book of Curious and Interesting Puzzles, 1992.