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**Proggy** Solve: $\displaystyle x^2 - 7y^2 = 3z^2$

I set it congruent (mod 3) to reduce it to $\displaystyle x^2 - y^2 \equiv 0 (mod 3)$

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 $\displaystyle -y^2 \equiv a^2 (mod 3)$ 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