Quote:
Originally Posted by SPWorley
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?
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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.