LATTICE POINTS ON THE HOMOGENEOUS CUBIC EQUATION WITH FOUR UNKNOWNS x2 - xy + y2 + 4w2 = 8z3

Authors

  • Manju Somanath Department of Mathematics,National College, Trichy, Tamilnadu, India
  • Radhika Das Department of Basic Sciences & Humanities,Rajagiri school of Engineering & Technology, Kerala, India https://orcid.org/0000-0002-5703-2762
  • Bindu V.A Department of Basic Sciences & Humanities,Rajagiri school of Engineering & Technology, Kerala, India

DOI:

https://doi.org/10.29121/granthaalayah.v8.i8.2020.932

Keywords:

Homogeneous Cubic Equation, Lattice Points, Integral Solutions, Special Polygonal Numbers

Abstract [English]

The Homogeneous cubic equation with four unknowns represented by the equation x2 - xy + y+ 4w= 8z3  is analyzed for its patterns of non zero distinct integral solutions. Here we exhibit four different patterns. In each pattern we can find some interesting relations between the solutions and special numbers like Polygonal number, Three-Dimensional Figurate number, Star number, Rhombic Dodecahedral number etc.

Downloads

Download data is not yet available.

References

L.E. Dickson, “History of Theory of Numbers”, Volume 2, Chelsea Publication Company, Newyork, 1952.

M.A. Gopalan., V. Sangeetha and Manju Somanath, “Lattice Points on the Homogeneous Cubic Equation with Four Unknowns x^2-xy+y^2+3w^2=7z^3”, International Journal of Computational Engineering Research, Volume 03,2013,24-26.

M. Somanath, J.Kannan, K. Raja and V. Sangeetha, “On the integer solution of the Pell Equation x^2=17y^2-19^t, JP Journal of Applied Mathematics, Volume 2,2017,81-88.

M. Somanath and J.Kannan, “On a class of solution for a Diophantine Equation of second degree”, International Journal of Pure and Applied Mathematics, ,Volume12, 2017, 55-62.

M. Somanath and J.Kannan, “On the Positive Integer Solution for a Diophantine Equation”, Journal of Mathematics and Informatics, Volume 10, 2017,173-177. DOI: https://doi.org/10.22457/jmi.v10a23

D. M. Burton, “Elementary Number Theory”, Tata Mc-Graw-Hill Ed.2012.

J. Kannan, M. Somanath, K. Raja, “Solution of negative Pell equation involving twin prime”, JP Journal of Algebra, Number Theory and Applications, Volume 5,2018, 869-874. DOI: https://doi.org/10.17654/NT040050869

Downloads

Published

2020-08-26

How to Cite

Somanath, M., Das, R., & Bindu, V. (2020). LATTICE POINTS ON THE HOMOGENEOUS CUBIC EQUATION WITH FOUR UNKNOWNS x2 - xy + y2 + 4w2 = 8z3. International Journal of Research -GRANTHAALAYAH, 8(8), 135–139. https://doi.org/10.29121/granthaalayah.v8.i8.2020.932