Re: Factoring polynomials over binary field

In article <gerry-9D8241.09000316032006@xxxxxxxxxxxxxxxxxx>,
Gerry Myerson <gerry@xxxxxxxxxxxxxxxxxxxxxxxxx> wrote:

In article <1142448656.280356.154440@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
"Yaroslav Bulatov" <yaroslavvb@xxxxxxxxx> wrote:

When can a polynomial of the form 1+x+x^2+...+x^{n-1}, with n prime be
factored over binary field? For instance they factor for n equal to 7,
17, 23 but not for 3, 5, 11

1+x+x^2+x^3+x^4+x^5+x^6 = (1+x^2+x^3)(1+x+x^3)

Irreducible if and only if 2 is a primitive root mod n?

Is this an exercise in some number-theory book or something? I answered
the same question at least once a few months ago in sci.math.research.
(Same answer as Gerry's of course!)

dave
.

Relevant Pages

  • Re: On localization rings
    ... Trav wrote: ... Yes, well as Lee Rudolph once noted, the statement above will ... eventually be attributed to Gerry Myerson. ...
    (sci.math)
  • Re: Dave Rusin, Fermat, and Fermats Last Theorem
    ... Gerry Myerson responded to a thread ... I had not seen yet (killfiles in operation!) so I now saw the line: ... You may draw your own conclusions. ...
    (sci.math)
Quantcast