The integer part of a nonlinear form with integer variables.

Using the Davenport-Heilbronn method, we show that if $\lambda_{1},\lambda_{2},\ldots,\lambda_{9}$ are positive real numbers, at least one of the ratios $\lambda_{i}/\lambda_{j}$ ( $1\leq i< j\leq9$) is irrational, then the integer parts of $\lambda_{1}x_{1}^{3}+\lambda_{2}x_{2}^{3}+\lambda_{3}x_{3}^{4}+\lambda_{4}x_{4}^{4} +\lambda_{5}x_{5}^{5}+\cdots+\lambda_{9}x_{9}^{5}$ are prime infinitely often for natural numbers $x_{1},x_{2},\ldots,x_{9}$. [ABSTRACT FROM AUTHOR]