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  • Cletus Emmanuel
    Hi all, (1) Proth s theorem states: Let n = h.2k+1 with 2k h. If there is an integer a such that a(n-1)/2 = -1 (mod n), then n is prime. (2) Now, is there
    Message 1 of 3 , Dec 2, 2003
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      Hi all,
      (1) Proth's theorem states:
      Let n = h.2k+1 with 2k > h. If there is an integer a such that a(n-1)/2 = -1 (mod n), then n is prime.

      (2) Now, is there a theorem which states?:
      Let n = h.2k - 1 with 2k > h. If there is an integer a such that a(n-1)/2 = 1 (mod n), then n is prime.

      If there is no theorem for (2), can anyone prove or disprove it?.....

      ---Cletus Emmanuel


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    • jbrennen
      ... a(n-1)/2 = 1 (mod n), then n is prime. ... As I indicated to the poster in a private response, disprove this statement with n=175, h=11, k=4, a=51.
      Message 2 of 3 , Dec 2, 2003
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        --- Cletus Emmanuel <cemmanu@y...> wrote:
        > (2) Now, is there a theorem which states?:
        > Let n = h.2k - 1 with 2k > h. If there is an integer a such that
        a(n-1)/2 = 1 (mod n), then n is prime.
        >
        > If there is no theorem for (2), can anyone prove or disprove it?.....

        As I indicated to the poster in a private response,
        disprove this statement with n=175, h=11, k=4, a=51.
      • richard_heylen
        ... it?..... ... Or indeed any composite n of the above form with a=1! Rick
        Message 3 of 3 , Dec 2, 2003
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          --- In primenumbers@yahoogroups.com, "jbrennen" <jack@b...> wrote:
          > --- Cletus Emmanuel <cemmanu@y...> wrote:
          > > (2) Now, is there a theorem which states?:
          > > Let n = h.2k - 1 with 2k > h. If there is an integer a such that
          > a(n-1)/2 = 1 (mod n), then n is prime.
          > >
          > > If there is no theorem for (2), can anyone prove or disprove
          it?.....
          >
          > As I indicated to the poster in a private response,
          > disprove this statement with n=175, h=11, k=4, a=51.

          Or indeed any composite n of the above form with a=1!

          Rick
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