Re: irreducible polynomial in Z_7[t] roots of which are primitive in GF(49)

From: anonymous.rubbertube@xxxxxxxxx
Date: Fri, 14 Nov 2008 05:22:39 -0800 (PST)

On Nov 14, 7:57 am, Kenneth Bull <kenneth.b...@xxxxxxxxx> wrote:

How to find an irreducible polynomial in Z_7[t] roots of which are
primitive in GF(49) >

Primitives in GF(p^n) are primitive (p^n - 1)th roots of unity; so to
get a polynomial in Z_p[t] whose roots are primitives in GF(p^n), try
a polynomial whose splitting field is the degree n unramified
extension of Z_p. In your case, I think the 48th (48 = 7^2 - 1)
cyclotomic polynomial does it.
.

Follow-Ups:
- Re: irreducible polynomial in Z_7[t] roots of which are primitive in GF(49)
  - From: Derek Holt

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- irreducible polynomial in Z_7[t] roots of which are primitive in GF(49)
  - From: Kenneth Bull

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