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Re: Is this a generalization of Fermat's Little Theorem?

From quasi <quasi@null.set>
Newsgroups sci.math
Subject Re: Is this a generalization of Fermat's Little Theorem?
Date 2015-08-14 16:42 -0400
Organization none
Message-ID <gckssadoie05ubpgcl3luim4o73libmn58@4ax.com> (permalink)
References <2015081323202939176-delaneyrm@earthlnknet>

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Robert Delaney wrote:
>
>In the thread “An Almost Theorem” on Compuserve²s SciMath forum:
>
>http://forums.compuserve.com/discussions/The_Science_and_Math_Forum/_/_/ws-sciencemath/130471.1 
>
>Alan Listoe proves this theorem for an integer square matrix A 
>of size n, prime p, and integer k:
>
>“A is semisimple over GF(p) if and only if there is a k such 
>that A^(p^k) = A (mod p).”

I don't think it's true.

Let n = 2, p = 3, A = [[0,-1],[1,-1]].

Then A is semisimple, but A^3 = I, hence there are no integers
k such that A^(p^k) = A (mod p).

quasi

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Thread

Is this a generalization of Fermat's Little Theorem? Robert Delaney <delaneyrm@earthlnk.net> - 2015-08-13 23:20 -0500
  Re: Is this a generalization of Fermat's Little Theorem? Robert Delaney <delaneyrm@earthlnk.net> - 2015-08-13 23:53 -0500
  Re: Is this a generalization of Fermat's Little Theorem? Robert Delaney <delaneyrm@earthlnk.net> - 2015-08-14 00:31 -0500
  Re: Is this a generalization of Fermat's Little Theorem? Simon Roberts <retenshun@twc.com> - 2015-08-14 11:34 -0400
    Re: Is this a generalization of Fermat's Little Theorem? Simon Roberts <retenshun@twc.com> - 2015-08-14 11:52 -0400
      Re: Is this a generalization of Fermat's Little Theorem? quasi <quasi@null.set> - 2015-08-14 15:02 -0400
      Re: Is this a generalization of Fermat's Little Theorem? Simon Roberts <retenshun@twc.com> - 2015-08-14 15:21 -0400
  Re: Is this a generalization of Fermat's Little Theorem? Robert Delaney <delaneyrm@earthlnk.net> - 2015-08-14 15:21 -0500
    Re: Is this a generalization of Fermat's Little Theorem? abu.kuanysh05@gmail.com - 2015-08-15 16:31 -0700
  Re: Is this a generalization of Fermat's Little Theorem? quasi <quasi@null.set> - 2015-08-14 16:42 -0400
    Re: Is this a generalization of Fermat's Little Theorem? Robert Delaney <delaneyrm@earthlnk.net> - 2015-08-14 20:01 -0500
      Re: Is this a generalization of Fermat's Little Theorem? Waldek Hebisch <hebisch@antispam.uni.wroc.pl> - 2015-08-15 18:04 +0000
        Re: Is this a generalization of Fermat's Little Theorem? quasi <quasi@null.set> - 2015-08-15 15:04 -0400
          Re: Is this a generalization of Fermat's Little Theorem? quasi <quasi@null.set> - 2015-08-15 16:41 -0400
            Re: Is this a generalization of Fermat's Little Theorem? quasi <quasi@null.set> - 2015-08-15 17:33 -0400
  Re: Is this a generalization of Fermat's Little Theorem? Simon Roberts <retenshun@twc.com> - 2015-08-15 02:57 -0400
    Re: Is this a generalization of Fermat's Little Theorem? Simon Roberts <retenshun@twc.com> - 2015-08-15 18:43 -0400
  Re: Is this a generalization of Fermat's Little Theorem? Robert Delaney <delaneyrm@earthlnk.net> - 2015-08-15 20:49 -0500
    Re: Is this a generalization of Fermat's Little Theorem? quasi <quasi@null.set> - 2015-08-16 02:59 -0400
      Re: Is this a generalization of Fermat's Little Theorem? Timothy Murphy <gayleard@eircom.net> - 2015-08-16 12:28 +0200
        Re: Is this a generalization of Fermat's Little Theorem? quasi <quasi@null.set> - 2015-08-16 06:32 -0400

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