International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 14, Pages 2217-2226

Nonextendibility of D(1)-triples of the form {1,10,c}

Alan Filipin

Department of Mathematics, Faculty of Civil Engineering, University of Zagreb, Fra Andrije Kačića-Miošića 26, Zagreb 10000, Croatia

Received 4 March 2005; Revised 21 June 2005

Copyright © 2005 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.


We prove that there do not exist different positive integers c,d>1 such that the product of any two distinct elements of the set {1,10,c,d} diminished by 1 is a perfect square.