- #1
Animuo
- 13
- 0
Homework Statement
The product of any 4 consecutive integers will be one less than a perfect square.
Homework Equations
Well, a perfect square is a number that can be broken down to n*n where n is an integer.
If a number is consecutive to another number that means it is exactly one more than the other.
The Attempt at a Solution
So you substitute n for "any integer" and you get this
(n) (n+1) (n+2) (n+3)
I wasn't sure where to go from here I tried making it into a big polynomial and just got confused. The basic idea is that you want to somehow group these numbers together to get two equivalent parts (contained in parentheses) minus one. I've tried several different ways of doing this but for some reason I can't figure it out... I'll let you guys do the work :), thanks ahead of time