Solve for x,y: $x^2+1=2y^2$

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Solve for integers $x,y$ such that $x^2+1=2y^2$?

I tried factoring as $(x-y)(x+y)=(y-1)(y+1)$ but couldn't continue from here, I would appreciate any help.

Thanks!

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Look up Pell's equation. This is a variant, the negative Pell equation.