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semi-primes

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  • Kermit Rose
    Obvious typo in the statement of my theorem is corrected here. If P is the product of two primes, x and y, P = x y, then for any relatively prime integer b, to
    Message 1 of 1 , Jun 23, 2012
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      Obvious typo in the statement of my theorem is corrected here.

      If P is the product of two primes, x and y,

      P = x y,

      then
      for any relatively prime integer b, to P,

      b^(P+1) = b^(x+y) mod P.

      Proof:

      The number of positive integers< P that are
      relatively prime to P is (x-1)(y-1).

      By fundamental group theory theorem,
      for any relatively prime integer b, to P,

      b^( (x-1)(y-1)) = 1 mod P.

      b^(x y - y - x + 1) = 1 mod P.

      b^(x y + 1 - (x+y) ) = 1 mod p

      b^(x y + 1) = b^(x+y) mod P

      b^(P + 1) = b^(x+y) mod P.




      Kermit
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