Coprimeness-preserving discrete KdV type equation on an arbitrary dimensional lattice

We introduce an equation defined on a multi-dimensional lattice, which can be considered as an extension to the coprimeness-preserving discrete KdV like equation in our previous paper. The equation is also interpreted as a higher-dimensional analog of the Hietarinta–Viallet equation, which is famous for its singularity confining property while having an exponential degree growth. As the main theorem, we prove the Laurent and the irreducibility properties of the equation in its “tau-function” form. From the theorem, the coprimeness of the equation follows. In Appendixes A–D, we review the coprimeness-preserving discrete KdV like equation, which is a base equation for our main system, and prove the properties such as the coprimeness.