Abstract
Recently, P. Kaplan and K. S. Williams [10] considered (as an example) the representation of primes by binary quadratic forms of discriminant –768. These forms fall into 4 genera, each consisting of two classes. In particular, they considered the formsF=3X2+642 and G = 12X2+12XY+19Y2.It follows from genus theory (as explained in [10]) that every prime p ≡ 19 mod 24 is represented by exactly one of the forms F and G. Based on numerical data, they conjectured that a prime p ≡ 19 mod 24 is represented bywhereVo = 2, V1 = -4, Vn+2=-4Vn+1 -Vn (n∨0).
Publisher
Cambridge University Press (CUP)
Reference10 articles.
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