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I'm trying to prove that $a^n+1$ can only be prime if $n$ is a power of $2$. Is there a general factorization of $a^n+1$?

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    If $n$ is prime then you have $a^n + 1 = (a + u_n^1)(a + u_n^2)\cdots(a + u_n^n)$ where $u_n$ is an $n$th root of unity.2011-03-22

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