Article overview
Abstract
Let k be a natural number. Two integers α and β are said to have the property D(k) (resp. D(-k)) if αβ+k (resp. αβ-k) is a perfect square. The purpose of this paper is identi cation of polynomials producing quadruples with property D(k) for certain values of k. Incidentally the paper brings out an at- tribute of Ramanujan number 1729 in contributing two quadruples of polynomials with property D(k).
Keywords and Phrases
Property pkextendable setPrk sequencePell's equationquadruple with Diophantine propertyRamanujan number.
AMS Subject Classification
11B37, 11B83, 11D09.
Reference information
How to Cite
A.M.S. Ramasamy (2019). POLYNOMIALS YIELDING QUADRUPLES WITH PROPERTY D(k). Journal of Ramanujan Society of Mathematics and Mathematical Sciences, 7(1), 53-64.