Solutions to equation (or proof that there is no solution) I am unable to find a solution or prove that there is none. I really need help:
$a, b,$ and $c$ are positive integers such that
$a^2-b^2+c^2=2.$
Is this possible? If possible find the solutions, if not prove that there is no solutions.

To search for a positive answer to such a question, Wolfram Alpha is your friend. In your case, $a=c=3$ and $b=4$ is a solution (the only positive integer solution Wolfram Alpha was able to find, though that is not proof it is unique).
