International Journal of Mathematics and Mathematical Sciences
Volume 2007 (2007), Article ID 63739, 12 pages
Extensions of Some Parametric Families of -Triples
Faculty of Civil Engineering, University of Zagreb, Fra Andrije Kačića-Miošića 26, Zagreb 10000, Croatia
Received 7 September 2006; Revised 24 November 2006; Accepted 29 November 2006
Academic Editor: Dihua Jiang
Copyright © 2007 Alan Filipin. 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.
Let be an integer. A set of positive integers is called a --tuple if the product of any two of them increased by is a perfect square. In this paper, we consider extensions of some parametric families of -triples. We prove that if for is a -quadruple, then . Furthermore, if , for , is a -quadruple, then . But for , this statement is not valid. Namely, the -triple has exactly two extensions to a -quadruple: and .