  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.
