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JdotAckdot
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I've been able to prove that the set {8n+7} has infinite primes by manipulating Fermat's Theorem, but I'm trying to reprove it using quadratic residue and Legendre Polynomials.
I've been able to show that for p=8n+7, (2/p)=1 and (-1,p)=-1
So it follows that (-2/p)=-1. And that (-2/p)=1 iff p congruent to 1 or 5 mod 8.
any ideas how to extend that to the final proof?
I've been able to show that for p=8n+7, (2/p)=1 and (-1,p)=-1
So it follows that (-2/p)=-1. And that (-2/p)=1 iff p congruent to 1 or 5 mod 8.
any ideas how to extend that to the final proof?