Generalized Pell equation ($x^2-d{y}^2=N$)

A generalized Pell equation is $x^2-d{y}^2=N$ 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.