A pell equation is an equation [itex] x^2-dy^2=1 [/itex] where d is a positive integer that is not a perfect square. Can you figure out why we do not want d to be a perfect square?
The Attempt at a Solution
if d was a perfect square then we would have
[itex] x^2-d^2y^2=1 [/itex] z=dy then [itex] x^2-z^2=1=(x+z)(x-z)=1 [/itex]
x>z for this to work so if x>z then x-z is at least 1 and then x+z would be bigger than 1
so (x+z)(x-z)>1 so this wont work so d cant be a perfect square. Does this work?