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  • najibaamimar
    Hello all! Can anyone give me a reference(if possible on the web) of the following theorem: Let p be prime, d=2*p*j+1, d=1(mod 8) and j even, then x^{2j}=2
    Message 1 of 2 , Mar 13, 2008
      Hello all!

      Can anyone give me a reference(if possible on the web) of the
      following theorem:
      Let p be prime, d=2*p*j+1, d=1(mod 8) and j even, then
      x^{2j}=2 (mod d) is solvable if and only if 2^p=2^{(d-1)/(2j)}=1 (mod d)

      Thanks a lot
    • Adam
      Let p=3, j=8, so d=49. x=16 and 33 solve x^16=2 mod 49 2^3 mod 49 is obviously not 1 Adam ... (mod d)
      Message 2 of 2 , Mar 13, 2008
        Let p=3, j=8, so d=49.

        x=16 and 33 solve x^16=2 mod 49
        2^3 mod 49 is obviously not 1

        Adam

        --- In primenumbers@yahoogroups.com, "najibaamimar"
        <najibaamimar@...> wrote:
        >
        > Hello all!
        >
        > Can anyone give me a reference(if possible on the web) of the
        > following theorem:
        > Let p be prime, d=2*p*j+1, d=1(mod 8) and j even, then
        > x^{2j}=2 (mod d) is solvable if and only if 2^p=2^{(d-1)/(2j)}=1
        (mod d)
        >
        > Thanks a lot
        >
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