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$\begingroup$

Motivated by this problem, and KCd's comment on my answer, I am left with the following question:

Question: Suppose that $n\not \equiv 2\pmod{3}$. Is $x^n+x+1$ irreducible over $\mathbb{Q}$?

I am not sure how to solve this, any thoughts are appreciated.

  • 3
    Sorry ignored the modulo condition given.2012-12-25

1 Answers 1

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Yes, it is true. See the second claim of Theorem 1 on page 289.

  • 7
    +1. Improvement suggestion: Add the word "Yes" to the answer.2012-12-25