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Let $l$ be an odd prime number. Let $f(X) = 1 + X + ... + X^{l-1} \in \mathbb{Z}[X]$. Probably Gauss was the first man who proved that $f(X)$ is irreducible. I wonder how he proved it.

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    Yes, I think I have seen that mentioned too. But everyone knows the name of Eisenstein's criterion.2012-07-23

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The first proof presented here is a proof by Gauss. The original is in Gauss' magnum opus Disquisitiones Arithmeticae.

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    That's great. Thanks!2012-07-23