From: "Everett W. Howe"
Subject: Re: A ternary quadratic form
Date: Thu, 18 Nov 1999 03:06:31 GMT
Newsgroups: sci.math.research
Keywords: representation of integers by x^2 + 3(y^2 + z^2)
"Imre Z. Ruzsa" wrote:
> Recently I came across the following question: which positive integers
> can be represented as x^2 + 3(y^2 + z^2) , with integers x,y,z. It is
> easy to see that no integer of the form 9^k (3a+2) has such a
> representation, and I conjecture that every other integer has one.
> Some calculations support this.
> I looked in the literature and found results on many similiar forms, but
> not on this one. I would appreciate any reference.
This is Theorem IV (page 65) of
L. E. Dickson, Integers represented by positive ternary quadratic
forms, Bull. Amer. Math. Soc. 33 (1927), 63--70.
> Karoly Boroczki and I could apply this to the following question: for
> what values of k and n is there a convex lattice hexagon with k lattice
> points inside and n on the boundary.
What can you prove?
-- Everett
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