View Single Post
Old 2009-08-25, 09:46   #2
R.D. Silverman
R.D. Silverman's Avatar
Nov 2003

26×113 Posts

Originally Posted by SPWorley View Post
I'm playing with cubic reciprocity formulas.

From that link, it states "A theorem of Fermat states that every prime p ≡ 1 (mod 3) is the sum of a square and three times a square: p = a^2 + 3b^2"

How would you go about finding a and b given p?


Factor p over Q(sqrt(-3)). See H. Cohen's book on Algebraic Number Theory.
I believe that a variation of Cornachia'a algorithm is used, but my memory
could be faulty. It's been a long time since I looked at this kind of stuff.
R.D. Silverman is offline   Reply With Quote