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25223Re: Fermat+Euler+Frobenius

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  • djbroadhurst
    Jul 18 5:10 AM
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      --- In primenumbers@yahoogroups.com,
      "paulunderwooduk" <paulunderwood@...> wrote:

      > > David, sorry for the noise. Here is what I have in mind:
      > Oh dear, I meant ...
      > Paul -- suffering from error-after-posting syndrome

      After tidying up your request, the Gremlims happily obliged:

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

      {tst(n,a)=local(Q=3*a^2+1);kronecker(a^2-1,n)==-1&&wriggle(a,n)&&
      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);}

      {if(tst(9526822969*133375521553,244578343630781166947),
      print(" Gremlins rule OK"));}

      Gremlins rule OK

      David (their minder)
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