Here is the original theorem from my book (A Course in Number Theory by H.E.Rose, 2nd edition):
Let $a>1$ and $c>1$ be integers. The integer $a^c-1$ is composite if $a>2$ or if $c$ is composite.
I am having trouble understanding part of the proof for this theorem. I understand that if $c$ is composite then $a^c-1$ is also composite. My book, however, does not provide much explanation for why $a^c-1$ is composite if $a>2$. I tried working it out myself and have come to the conclusion that if $a>2$ and $a$ is odd, then $a^c-1$ is even and therefore must be composite. I'm stuck with the case for $a>2$ and $a$ is even.