Observations on the equation y2=312x2+1

Dr. G.Sumathi

doi:https://doi.org/10.14445/22315373/IJMTT-V50P538

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 50 | Number 4 | Year 2017 | Article Id. IJMTT-V50P538 | DOI : https://doi.org/10.14445/22315373/IJMTT-V50P538

Observations on the equation y2=312x2+1

Dr. G.Sumathi

Abstract

The binary quadratic equation y2=312x2+1 is considered and a few interesting properties among the solutions are presented. Employing the integral solutions of the equation under consideration, a few patterns of Pythagorean triangles and rectangles are observed.

Keywords

Binary, Quadratic, Pyramidal number, Integral Solutions.

References

[1] Dickson L.E,History of Theory of numbers,Vol.2,Chelsea publishing company,Newyork,1952.
[2] Mordel L.J, Diophantine Equations, Academic press,Newyork,1969.
[3] Telang S.J,Number theory,Tata Mcgraw Hill Publishing Company Limited, New Delhi,2000.
[4] David Burton,Elementary Number Theory, Tata Mcgraw Hill ,Publishing Company Limited, New Delhi,2002.

Citation :

Dr. G.Sumathi, "Observations on the equation y2=312x2+1," International Journal of Mathematics Trends and Technology (IJMTT), vol. 50, no. 4, pp. 231-234, 2017. Crossref, https://doi.org/10.14445/22315373/IJMTT-V50P538