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25221Re: Fermat+Euler+Frobenius

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  • paulunderwooduk
    Jul 18, 2013
      David, sorry for the noise. Here is what I have in mind:

      {wriggle(a,n)=local(v=[a,3*a^2+1,5*a^2-1,13*a^2-1,7*a^2-3]);
      sum(k=1,#v,gcd(v[k],n)>1)==0;}

      with

      {tst(n,a)=kronecker(a^2-1,n)==-1&&
      gcd(a,n)==1&&
      Mod(a,n)^(n-1)==1&&
      Mod(a-1,n)^((n-1)/2)==kronecker(a-1,n)&&
      Mod(a+1,n)^((n-1)/2)==kronecker(a+1,n)&&
      Mod(3*a^2+1,n)^((n-1)/2)==kronecker(3*a^2+1,n)&&
      Mod(Mod(1,n)*L,L^2-lift(Mod((10*a^2-2)/(3*a^2+1),n))*L+1)^((n+1)/2)==kronecker(3*a^2+1,n)
      ;}

      Paul
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