Homework Statement
Find all integer solutions to x2 + y2 + z2 = 51. Use "without loss of generality."
Homework Equations
The Attempt at a Solution
My informal proof attempt:
Let x, y, z be some integers such that x, y, z = (0 or 1 or 2 or 3) mod 4
Then x2, y2, y2 = (0 or 1) mod 4
So x2 +...