Generalized Pell equation
= Generalized Pell equation
{title2=$x^2-dy^2=N$}
A generalized Pell equation is $x^2-dy^2=N$ for a fixed nonsquare positive integer $d$ and nonzero integer $N$. Multiplication by units of a real <quadratic number field> preserves the norm up to sign, reducing solutions to finitely many unit orbits when an appropriate bounded reduction interval is used.