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I understand that this is true.

Primes are always odd so a would naturally have to be even, if $1$ is being added to it.

For example, $4^2+1 = 17$.

But I'm not quite sure how to prove this.

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    Do you mean the $a$ is even part? You have just proved that. If $a>1$ is odd, then $a^n+1$ is even and greater than $2$, so cannot be prime. (One could add, because it is divisible by $2$ and greater than $2$, but I think that hardly needs saying.) The somewhat harder part is showing that $n$ is a power of $2$? Is that the part you are asking about?2012-12-10

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