论文标题
由多线性多项式代表整数
Representing integers by multilinear polynomials
论文作者
论文摘要
令$ f（\ boldsymbol x）$为$ n \ ge 1 $度量的均质多项式，$ 1 \ leq d \ leq d \ leq d \ leq n $具有整数系数，因此其每个变量的度量等于$ 1 $。我们在$ f $上提供一些足够的条件，以确保存在一个整数$ b $，存在一个整数矢量$ \ boldsymbol a $，以便$ f（\ boldsymbol a）= b $。提供的条件还保证了vector $ \ boldsymbol a $可以以有限数量的步骤找到。
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.
