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International Journal of Mathematics and Mathematical Sciences
Volume 8 (1985), Issue 4, Pages 799-804
http://dx.doi.org/10.1155/S0161171285000886

On k-traid sequences

1Panjab University, Chandigarh 160014, India
2Department of Mathematics and Statistics, University of New Brunswick, Fredericton E3B 5A3, Canada

Received 29 May 1984; Revised 29 June 1984

Copyright © 1985 Hindawi Publishing Corporation. 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

At the conference of the Indian Mathematical Society held at Allahabad in December 1981, S. P. Mohanty and A. M. S. Ramasamy pointed out that the three numbers 1, 2, 7, have the following property: the product of any two of them increased by 2 is a perfect square. They then showed that there is no fourth integer which hsares this property with all of them. They used Pell's equation and the theory of quadratic residues to prove their statement. In this paper, we show that their statement holds for a very large set of triads and our proof of the statement is very simple.