Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » sci.math.* » sci.math.independent

Topic: Is x^n + (x+2)^n irreducible over Q if n is a power of 2?
Replies: 10   Last Post: Sep 12, 2006 12:43 AM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Edwin Clark

Posts: 673
Registered: 12/3/04
Re: Is x^n + (x+2)^n irreducible over Q if n is a power of 2?
Posted: Sep 11, 2006 9:04 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

> One can prove it using Eisenstein, however, and that's probably the
> best way.


I still prefer Peter's solution since it can be modified to show
that if r is any nonzero rational number and n is any power of
2 then
p(x) = x^n + (x+r)^n

is irreducible over Q.

Can that be done with Eisenstein's Criterion? :-)

Anyhow, thanks to all who responded.

Edwin




Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.