\\Compute the group H from Problems 11-13 of the problem list
\\Subgroup of Z/n[sqrt(d)]^* where (a+b*sqrt(d))^n = a-b*sqrt(d)
\\sqrt(d) is given by z below. Output is a vector of vectors [a,b].
{
set_h(n,d)=local(v,z);v=[];z=Mod(Mod(1,n)*x,Mod(1,n)*(x^2-d));
forvec(a=vector(2,j,[0,n-1]),
   if(gcd(a[1]^2-d*a[2]^2,n)==1&&
   (Mod(a[1],n)+z*Mod(a[2],n))^n==(Mod(a[1],n)-z*Mod(a[2],n)),
   v=concat(v,[a]))
);v
}

\\The test in the AKS conjecture
{
test(n,r)=
if(Mod(Mod(1,n)*(x+1),Mod(1,n)*(x^r-1))^n==Mod(Mod(1,n)*(x^(n%r)+1),Mod(1,n)*(x^r-1)),1,0)
}