How to check if $ x^2 + x = y^2 - 1$ has positive integer solutions? How to check if $ x^2 + x = y^2 - 1$ has positive integer solutions?
I've tried using different modulos to simplify problem, but nothing has worked yet.

Let $x,y$ be such that $x$ is a positive integer and $x^2+x+1=y^2$.  $$x^2<x^2+x+1<x^2+2x+1\\x^2<y^2<(x+1)^2$$ 
So clearly $y$ cannot be also be a positive integer since there are no positive integers between $x$ and $x+1$.
