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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

 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

> 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

Date Subject Author
9/10/06 Edwin Clark
9/10/06 Peter L. Montgomery
9/10/06 Edwin Clark
9/10/06 G. A. Edgar
9/10/06 Jannick
9/10/06 Ignacio Larrosa CaÃ±estro
9/11/06 Jannick
9/11/06 Gene Ward Smith
9/11/06 Jannick
9/11/06 Edwin Clark
9/12/06 Gene Ward Smith