a) Prove that if and 4|n, then x, y, and z are even.
b) Prove that if n is of the form , then n is NOT the sum of three squares.
How can we prove part a?
For part b, this is what I've got so far.
Suppose n is a sum of three squares (aim for a contradiction). Assuming the result of part a, since 4| , x,y, and z must be even, so x/2, y/2, z/2 are integers.
=> , so n/4 is also a sum of three squares
How to finish the proof from here?
Any help is appreciated!
[note: also under discussion in math links forum]