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On certain quaternary quadratic forms
Published 14 Nov 2014 in math.NT | (1411.6963v1)
Abstract: In this paper, we determine all the positive integers $a, b$ and $c$ such that every nonnegative integer can be represented as $$ f{a,b}_c(x,y,z,w)=ax2+by2+c(z2+zw+w2) \,\, \textrm{with} \,\,x,y,z,w\in\mathbb{Z}. $$ Furthermore, we prove that $f{a,b}_c$ can represent all the nonnegative integers if it represents $n=1,2,3,5,6,10.$
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