Pell's equation

Remarks

The pairs $(\pm 1, 0)$ are the trivial solutions. For $d = 2$, the pair $(3, 2)$ is a solution, since $9 - 2 \cdot 4 = 1$. A solution $(x, y)$ with $y \neq 0$ gives the rational approximation $x / y$ of $\sqrt{d}$. The name comes from an error of Euler, who attributed a solution by William Brouncker to John Pell.