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Forum: Abstract Algebra & Algebraic Number Theory 2018-09-22, 00:12
Replies: 7
Views: 6,107
Posted By science_man_88
If the order of 3 has to divide both, then it...

If the order of 3 has to divide both, then it divides their gcd . Which means factors of p-1 coprime with n, need to divide ord(-k) mod p to be the ord(3) mod p. Which for someone stupid like me...
Forum: Abstract Algebra & Algebraic Number Theory 2018-09-19, 17:30
Replies: 7
Views: 6,107
Posted By science_man_88
here's how I got what I did: 3^n+k\equiv 0...

here's how I got what I did:

3^n+k\equiv 0 \bmod p; 3^n\equiv -k \bmod p; (3^n)^{ord(-k)}\equiv 3^{n* ord(-k)}\equiv -k^{ord(-k)}\equiv 1\bmod p I realize now this needs to divide by the order of...
Forum: Abstract Algebra & Algebraic Number Theory 2018-09-19, 15:42
Replies: 7
Views: 6,107
Posted By science_man_88
https://primes.utm.edu/notes/proofs/MerDiv.html ...

https://primes.utm.edu/notes/proofs/MerDiv.html allows us to use the first step 3^n\equiv -k \bmod p which gets us that the order of -k mod p times n either divides or is divisible by the order of 3...
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