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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

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Registered: 12/6/04
Re: Is x^n + (x+2)^n irreducible over Q if n is a power of 2?
Posted: Sep 11, 2006 3:42 AM
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On 11.09.2006 00:10, Ignacio Larrosa Cañestro wrote:
> En el,
> Jannick Asmus <> escribió:

>> On 10.09.2006 20:02, Edwin Clark wrote:
>>> Is the polynomial x^n + (x+2)^n irreducible over Q if n is a power of
>>> 2?
>>> It is true at least for n = 2^k, k=1..10.

>> Let f(x)=x^n +(x+2)^n, then f(y-1)/2 is an Eisenstein polynomial
>> w.r.t. 2, hence irreducible over Q (cf.

> But the constant term in f(y - 1)/2 is 1 ... Then you can't apply Eisenstein
> criterion.

Oupps, that's right !!! Sorry, I was too tired and hasty last night.

Best wishes,

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