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# Pell's equation

(Redirected from Generalized Pell equation)

Pell’s equation[1] is a diophantine equation of the form

${\displaystyle x^{2}-Dy^{2}=1,\quad x,\,y\,\in \,\mathbb {Z} ,\,}$

for ${\displaystyle \scriptstyle D\,}$ a positive integer, not a square.

## Generalized Pell equation

The generalized Pell equation[2] is

${\displaystyle x^{2}-Dy^{2}=N,\quad x,\,y\,\in \,\mathbb {Z} ,\,}$

for ${\displaystyle \scriptstyle D\,}$ a positive integer, not a square, and ${\displaystyle \scriptstyle N\,}$ a nonzero integer.