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25214Re: Fermat+Euler+Frobenius

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  • djbroadhurst
    Jul 17, 2013
      --- In primenumbers@yahoogroups.com, "paulunderwooduk" <paulunderwood@...> wrote:

      > I notice Mod(a,n)^((n-1)/2) is neither 1 nor -1.

      Your latest wriggle is easily countered:

      {tst(n,a)=kronecker(a^2-1,n)==-1&&gcd(a,n)==1&&
      Mod(a,n)^((n-1)/2)==kronecker(a,n)&& \\ latest wriggle
      Mod(a-1,n)^((n-1)/2)==kronecker(a-1,n)&&
      Mod(a+1,n)^((n-1)/2)==kronecker(a+1,n)&&
      Mod(Mod(1,n)*(L+a),L^2-2*a*L+1)^(n+1)==3*a^2+1;}

      {n=47391041614253942746775474638243609594331524373222569350310\
      52914770672055547658535429075770110985428014024530096070179809;

      a=23229351387100192392009446875150639001986809695144905977925\
      121834927356460863740859375485138643249550235752142747141519;

      if(tst(n,a)&&!isprime(n),print(" Gremlins are still happy"));}

      Gremlins are still happy

      David (their minder)
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