# Find all $x$ for that $x^2 + (x+1)^2$ is a square

Answers: 1

Suppose $x^2 + (x+1)^2 = y^2$. We can revise it as $(2x+1)^2 + 1 = 2y^2$ or $(2x+1)^2 - 2y^2 = -1$.

If $z=2x+1$ after that we have $z^2 - 2y^2 = -1$. This is Pell's equation. Wikipedia write-up demonstrates how to address it.

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falagar 2019-05-09 09:00:30

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