On the universality of product for classes of linear functions of two variables

Earlier, the author introduced the concept of a universal function and proved the existence of universal functions for classes of linear $k$-valued functions of two variables for $k\ge5$. In this paper, we show that the product modulo $k$ is a universal function for the class of linear $k$-valued functions of two variables if and only if $k=6l\pm1$.