On 11.09.2006 00:10, Ignacio Larrosa Cañestro wrote: > En el mensaje:email@example.com, > Jannick Asmus <firstname.lastname@example.org> 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. >> http://en.wikipedia.org/wiki/Eisenstein%27s_criterion). >> > > 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.