Hi I've been stuck on this equation for a while. Pretty sure it has something to do with Pell's equation $x^2 - D y^2 = a$. Not exactly sure.
The question:
(i)Prove that there is only one solution to $x^2 = y^2 + 71$ for positive integers $x$ and $y$.
Then part (ii) which I'm capable of doing if I get (i):
(ii) Hence (and not otherwise) prove that there do not exist three consecutive integer values of $n$ for which $71n + 60$ is a perfect square.
If any of you could help me get (i) that would be great.
