Modular Arithmetic · Medium problem

$a^3 - b^3$ is divisible by $12$

$2^a \equiv 2^b \pmod{12}$

$a \equiv b \pmod{24}$

$a + b \equiv 0 \pmod{12}$

If $a, b$ are even, $\dfrac a2 \equiv \dfrac b2 \pmod{12}$