Power of 2^10 Minus Power of 10^3 is Divisible by 24

Theorem
Let $n \in \Z_{\ge 0}$ be a non-negative integer.

Then $2^{10 n} - 10^{3 n}$ is divisible by $24$.

That is:
 * $2^{10 n} - 10^{3 n} \equiv 0 \pmod {24}$