How to prove $\frac{2^a+3}{2^a-9}$ is not a natural number How can I prove that
$$\frac{2^a+3}{2^a-9}$$
for $a \in \mathbb N$ is never a natural number?

$$1+\frac{12}{2^a-9}$$
which means that $2^a$ should equal either $10,11,12,13,15$ or $21$, but neither of them is a power of $2$, so it's never a natural number
