Solve:

I set it congruent (mod 3) to reduce it to

This does not fit the sum of two squares theorem and I can not seem to find any difference of two squares theorem. Also, I can not make for any a, so I can not make it sum of two squares that way either.

The answer is supposed to be x=y=z=0, which is obvious. But setting it congruent (mod 3) seems to give me additional answers. How do I go about solving this problem? Thanks