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fermat mod mersenne 2^n+1 mod 2^m-1

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  • rach
    m integer 1 2^n+1 mod 2^m-1 the only solution is : 2^3+1 Mod 2^2-1 9 Mod 3 9 = 0 Mod 3 thanks
    Message 1 of 2 , May 23 11:55 AM
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      m integer >1

      2^n+1 mod 2^m-1

      the only solution is : 2^3+1 Mod 2^2-1

      9 Mod 3

      9 = 0 Mod 3
      thanks
    • Mark
      ... Remember that Fermat numbers are of the form 2^(2^a) + 1 . But if you want any positive exponent n (not of the form 2^a), then (2^1 + 1) mod (2^2 - 1) = 0
      Message 2 of 2 , May 24 8:10 AM
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        --- In primenumbers@yahoogroups.com, "rach" <maths_forall@...> wrote:
        >
        >
        > m integer >1
        >
        > 2^n+1 mod 2^m-1
        >
        > the only solution is : 2^3+1 Mod 2^2-1
        >
        > 9 Mod 3
        >
        > 9 = 0 Mod 3
        > thanks
        >

        Remember that Fermat numbers are of the form 2^(2^a) + 1 .

        But if you want any positive exponent n (not of the form 2^a), then


        (2^1 + 1) mod (2^2 - 1) = 0

        (2^3 + 1) mod (2^2 - 1) = 0 (yours)

        (2^5 + 1) mod (2^2 - 1) = 0

        etc.


        Mark
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