# Thread: Perfect Square combinatorics proof

1. ## Perfect Square combinatorics proof

Hello again!

If n is a positive integer and n > 1, prove that C(n,2) + C(n-1,2) is a perfect square.

Anyway, I went ahead and simplified the statement, which brought it to this:

$n^2 - 2n + 1$

In this form, it's fairly obvious that for any selected value of an integer n greater than one, it will be a perfect square.

What I'm wondering is if there's a better way to conclude the proof, or if that answer seems suitable.

since ${n^2} - 2n + 1 = (n-1)(n-1) = {(n-1)^2}$
any $n\in\\N : n>1$ will be a perfect square.