How to prove that $11...111$ is not the sum of two perfect squares I'm stuck with this problem: 
Show that $a=11...111$ is not the sum of two perfect squares. That is to say, there are no pair of  integers ($b$ , $c$) so that $b^2+c^2=a$. I think I am supposed to use equivalence classes in some way, but I do not know how to approach it.

It's easy to prove that every perfect square numbers, when is divided by 4, the remainder must be 0 or 1. And now the solution is clear.
