Discrete Mathematics - Modular Arithmetic

Question

Find all integers $x$, $y$ and $z$ so that $x^2 + y^2 + z^2 = 2xyz$.

I'm thinking to start with all congruences like this

2^(2) kon 3 its = 1 ,

3^(2) kon 3 = 0.

Trying to test all kind of numbers with power $2$?

It's that right to solve it?

After that i get stuck some clue??

Answer 1

Hint. Try to show that if $(x,y,z)$ is a solution then $x,y,z$ are all even numbers. This implies that $(0,0,0)$ is the only solution.