Diophantine equations, one of the interesting areas in
Number theory, occupy a pivotal role in the realm of mathematics and have a
wealth of historical significance. This chapter discusses on finding many
solutions in integers to the cubic equation with two unknowns given by \(a
(x-y)^3 = 8b x y\) ; \(a,b \in z -\) {0}, as the cubic equations fall into the
theory of elliptic curves. The substitution strategy is employed in obtaining
successfully different choices of solutions in integers. Some of the special
fascinating numbers are discussed in properties. These special numbers are
unique and have attractive characterization that sets them apart from other
numbers. The process of formulating second-order Ramanujan numbers with base
numbers as real integers is illustrated through examples. The process for
getting a sequence of Diophantine triples with suitable properties and Dio-3
tuples with suitable properties is illustrated.
Author(s) Details
N. Thiruniraiselvi
Department of Mathematics, School of Engineering and
Technology, Dhanalakshmi Srinivasan University Samayapuram, Trichy- 621 112,
Tamil Nadu, India.
https://orcid.org/0000-0003-4652-3846
Sharadha Kumar
Department of Mathematics, National College, Affiliated to
Bharathidasan University, Trichy-620 001, Tamil Nadu, India.
https://orcid.org/0000-0002-0509-6158
M. A. Gopalan
Department of Mathematics, Shrimati Indira Gandhi College,
Affiliated to Bharathidasan University, Trichy-620 002, Tamil Nadu, India.
https://orcid.org/0000-0003-1307-2348
Please see the book here:- https://doi.org/10.9734/bpi/rumcs/v8/529
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