International Journal of Mathematics and Mathematical Sciences
Volume 21 (1998), Issue 1, Pages 107-115
doi:10.1155/S0161171298000143
Integers representable by
(x+y+z)3/xyz
Department of Mathematics, University of Illinois, 1409 W. Green Street, Urbana 61801, IL, USA
Received 21 February 1996
Copyright © 1998 Sharon A. Brueggeman. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.