Year: 2020
Type: preprint
Abstract: Let $F(\boldsymbol x)$ be a homogeneous polynomial in $n \ge 1$ variables of degree $1 \leq d \leq n$ with integer coefficients so that its degree in every variable is equal to $1$. We give some sufficient conditions on $F$ to ensure that for every integer $b$ there exists an integer vector $\boldsymbol a$ such that $F(\boldsymbol a) = b$. The conditions provided also guarantee that the vector $\boldsymbol a$ can be found in a finite number of steps.
Source: arXiv (Cornell University)
Authors: Boettcher, Albrecht, Fukshansky, Lenny
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3042658772