On k-traid sequences

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.

Keywords

• Pell's equation
• congruence
• Fibonacci
• sequence.