24619Re: puzzle for a counterexample
- Nov 1, 2012Dear David,
thank you for your efforts,
i have the slight suspision that there may be counterexamples
for n=3 mod 4 but not for n=1 mod 4
even if i could not prove it.
I know that you are very fast in replying.
If you find one counterexample of the form n=1 mod 4
i would be glad to know it.
Sorry that i bother you with such a lot of questions,
but i hope that there will be some success.
Take your time.
p = 1 mod 4
> > the improved testNice Greetings from the primes
> > 1. gcd (a, p)=1
> > 2. Let jacobi (a, p) = -1
> > 3. let jacobi (a^2-a, p)=-1
> > 4. a^[(p-1)/2]=-1 mod p
> > 5. if (a+sqrt (a))^p = a-sqrt(a) mod p
> > 6. s+t*sqrt(a):=(a+sqrt (a))^[(p+1)/2] implies that
> > gcd (s, p)=1 or 0 or p, and gcd (t, p)=1 or 0 or p.
a lot of beautifull flowers in the mathematical universe
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