Kazuhide Matsuda
Published 2014-11-14Version 1
In this paper, we determine all the positive integers $a, b$ and $c$ such that every nonnegative integer can be represented as $$ f^{a,b}_c(x,y,z,w)=ax^2+by^2+c(z^2+zw+w^2) \,\, \textrm{with} \,\,x,y,z,w\in\mathbb{Z}. $$ Furthermore, we prove that $f^{a,b}_c$ can represent all the nonnegative integers if it represents $n=1,2,3,5,6,10.$
On $x(ax+1)+y(by+1)+z(cz+1)$ and $x(ax+b)+y(ay+c)+z(az+d)$
Several results on sequences which are similar to the positive integers
On sequences of positive integers having no $p$ terms in arithmetic progression
![QR code for arXiv:1411.6963 [math.NT]](http://oss.arxitics.com/images/favicon.svg)