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Old 2021-09-19, 06:18   #6
paulunderwood
 
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Sep 2002
Database er0rr

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[n, a, t, t2]=[8473, 2043, 140, 1252] gives a counterexample, but fear not, I have added gcd(a+t,n)==1 (to GT()) to stop degeneration of the determinant t*(t+a)+1 into unity, and gcd(t*a+1,n)==1 for a possibility of T.

Fixing the last practical test, tst_2_4 is now:

Code:
{
tst_2_4(n,a)=
kronecker(a^2-4,n)==-1&&
gcd(210,n)==1&&
gcd(a+2,n)==1&&gcd(2*a+1,n)==1&&
gcd(a+4,n)==1&&gcd(4*a+1,n)==1&&
gcd(a+8,n)==1&&gcd(8*a+1,n)==1&&
Mod(2,n)^(n-1)==1&&
Mod(Mod(x+2,n),x^2-a*x+1)^(n+1)==2*a+5&&
Mod(Mod(x+4,n),x^2-a*x+1)^(n+1)==4*a+17;
}

Last fiddled with by paulunderwood on 2021-09-19 at 06:41
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