Integers representable by (x+y+z)3/xyz

Abstract

In [1], A. Bremner and R. K. Guy discuss the problem of findin8 integers which may be represented by (x+y+z)3/xyz where X,Y,Z are integers. To this end, they present tables of solutions for integers n in the range −200≤n≤200 and offer several parametric solutions which involve both positive and negative integers. We present four infinite families of solutions which involve only positive intesers. Furthermore, these families contain sequences that are generated by linearly recursive relations.