Re: irreducible factors of x^n-1
- From: A-Man <shahabfaruqi@xxxxxxxxx>
- Date: Sat, 25 Jul 2009 02:31:02 EDT
Thank you. You have no idea how grateful I am. It was kind of you to reply. I do need to clarify a few things:
(1)As I understand you, the constructed polynomial h_{r+1} is the minimal polynomial of some b^p. Why are its other roots also of the type b^p; and so why are the b^p all conjugate to each other?
(2)Since b^p are the roots of the minimal poly and this minimal poly divides h_r(x) hence we have the sentence ''h_(r+1) and h_r have the same roots''. Where is the need for considering mod p^r here? Are we working in an extension of Z_{p^r}?
(3)Can you elaborate on the sentence: ''if you apply the Frobenius map enough times you can go from any one root to any other root.''
Regards.
.
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- Re: irreducible factors of x^n-1
- From: Arturo Magidin
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