International Journal of Mathematics and Mathematical Sciences
Volume 8 (1985), Issue 4, Pages 799-804
doi:10.1155/S0161171285000886
On k-traid sequences
Hansraj Gupta1
and K. Singh2
1Panjab University, Chandigarh 160014, India
2Department of Mathematics and Statistics, University of New Brunswick, Fredericton E3B 5A3, Canada
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.