Recent content by JdotAckdot

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...

[FONT="Century Gothic"]Just a couple questions that I'd appreciate any help on. 1. if [(2^d) - 1] is prime, prove that d is prime as well. 2. Prove that (p-1)C(k) is congruent to (-1)^k mod p. I've started them both but ended up getting stuck. Any ideas? Thanks

(a^m^2 + 1) | (a^n^2 - 1) ? [FONT="Trebuchet MS"]I'm sure there is a quick trick I'm missing somewhere... but anyone have any ideas on how to prove: (a^m^2 + 1) | (a^n^2 - 1) , for n > m. [Show [a^(n^2) -1] is divisible by [a^(m^2) +1] Thanks a lot. . . (I've tried letting k=n-m...

If you can help, that would be great. Let R be a commutative ring, and A,B,M be R-modules. Prove: a) HomR(A x B, M) is isomorphic to HomR(A, M) x HomR(B, M) b) HomR(M, A x B) is isomorphic to HomR(M, A) x HomR(M, B)