Pell's equation

This article page is a stub, please help by expanding it.

Pell’s equation is a diophantine equation of the form

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

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

Generalized Pell equation

The generalized Pell equation is

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

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

See also

• Index to OEIS: Section Pea#Pellian

External links

• Chu Wenchang, Regular polygonal numbers and generalized pell equations, Int. Math. Forum 2 (2007), no. 16, 781-802.