We prove that the product of 4 consecutive positive integers can't be a square number. We begin with a simpler proof for 2 consecutive integers, and also show the outline of a similar proof for 8 consecutive integers.

00:00 Intro
00:25 Simpler proof: n(n+1)
01:49 Main proof
04:33 Alternative conclusion
05:00 Addendum: n(n+1)...(n+7)