Loading ...
Sorry, an error occurred while loading the content.

25222Re: Fermat+Euler+Frobenius

Expand Messages
  • paulunderwooduk
    Jul 18, 2013
    • 0 Attachment
      --- In primenumbers@yahoogroups.com, "paulunderwooduk" <paulunderwood@...> wrote:
      >
      >
      > 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)
      > ;}
      >

      Oh dear, I meant

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

      Paul -- suffering from error-after-posting syndrome
    • Show all 24 messages in this topic