International Journal of Mathematics and Mathematical Sciences
Volume 21 (1998), Issue 1, Pages 107-115

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

Sharon A. Brueggeman

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.


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 200n200 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.