1
$\begingroup$

In my book text of Galois theory:

The polynomial $X^5-X-1$ over $\mathbb Z$. In $\mathbb F_5$ is irreducible.

Could you explain why?

Thanks.

$\endgroup$
0
$\begingroup$

This is an example of an Artin-Schreier polynomial. You can find general proofs about their irreduciblity in this thread and this thread.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.