The equation x2 Dy2 = N , with given integers D and
N and unknowns x and y , is called Pell’s equation.
If D is negative, it can have only a finite number of
solutions. If D is a perfect square, say D = a2 , the
equation reduces to x ay x ay = N and again
there is only a finite number of solutions. The most
interesting case of the equation arises when D 1 be a
positive non-square.