Irreducibility of $x^{n}+x+1$

Question

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.

Eric · Accepted Answer · 2012-12-26 00:15:27Z

up vote 12 down vote accepted

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

edited Dec 26 '12 at 0:15

Eric
33.3k576143

answered Dec 25 '12 at 7:38

alex.jordan
8,8441235

1

I found this by Googling "x^n+x+1 irreducible" which led me to this mathoverflow link. – alex.jordan Dec 25 '12 at 7:41

Very nice, thank you. – Eric Dec 25 '12 at 7:50

6

+1. Improvement suggestion: Add the word "Yes" to the answer. – user3533 Dec 25 '12 at 9:21

1 Answer