Prove that there are no positive integers $a$, $b$, and $c$ that satisfy the following equation: $a^2 + b^2 = 3c^2$

Prove that there are no positive integers $a$, $b$, and $c$ that satisfy the following equation: $$a^2 + b^2 = 3c^2.$$

Think about remainders modulo $3$ (Modular Arithmetic $\bmod 3$). What are the possible remainders of any perfect square when divided by $3$? Then, apply the method of Infinite Descent.