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RE Web--of--Ones

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  • Jose Ramón Brox
    ... From: Ignacio Larrosa Cañestro ... Because the product of quadratic residues is an inner product and (quadratic residue) *
    Message 1 of 1 , Mar 17, 2006
      ----- Original Message -----
      From: "Ignacio Larrosa Cañestro" <ilarrosa@...>


      >> ((B*2-1)^2+5)^2*5 == 4 (modulo p)
      >> In order for this to have solutions, 5 must be a quadratic
      >> residue modulo p, which eliminates primes p ending in 3 or 7.

      >Why?

      Because the product of quadratic residues is an inner product and (quadratic residue) *
      (quadratic non residue) = (quadratic non residue).

      Let be p>3. Then 4 is a quadratic residue modulo p, since it's 2^2 (mod p). If p=3, then
      4==1 = 1^2 (mod p), and if p=2, then 4 ==0 = 0^2 (mod p).

      So we have a equation of the form [(quadratic residue)*(quadratic residue)]*5 = (quadratic
      residue) (mod p) and therefore 5 must be a qr in order for the equation to have solutions.

      Regards. Jose Brox
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