A Review on Second Degree Homogeneous Diophantine Equation with Three Unknowns x2+y2=122z2

Abstract

The homogeneous ternary second degree equation given by x2+y2=122z2 is analysed for its non-zero distinct integral points on that. Completely various patterns of the equation into consideration are obtained by using python.

Introduction

Conclusion

In this paper, an bid has been created to get non-zero distinct integer results to the ternary quadratic Diophantine equation x 2 ? y 2 ?122 z 2 representing homogeneous cone with python canons. As there are kinds of cones, the compendiums might rummage around for indispensable kinds of cones to get integer results for the corresponding cones with python codes.

References

[1] L.E. Dickson, History of theory of Numbers, Vol. 2, Chelsea publishing Company, Newyork, 1952. [2] Mordel , Diophantine Equations, Academic press, Newyork, 1969. [3] Gopalan M.A., Geetha D,Lattice points on the hyperbola of two sheets x 2 ? 6xy ? y 2 ? 6x ? 2 y ? 5 ? z 2 ? 4, Impact J Sci Tech:4:23-32,2010. [4] Gopalan M.A., Vidhyalakshmi S,Kavitha A, Integral points on the homogeneous cone Diophantine J Math; 1(2):127-136, 2012. z 2 ? 2x 2 ? 7 y 2 , The [5] Gopalan M.A., Vidhyalakshmi S, Sumathi G,Lattice points on the hyperboloid of one sheet 4z 2 ? 2x 2 ? 3y 2 ? 4 , Diophantine J Math; 1(2): 109-115, 2012. [6] Gopalan M.A., Vidhyalakshmi S, Lakshmi K, Integral points on the hyprerboloid of two sheets 3y 2 ? 7x 2 ? z 2 ? 21 , Diophantine J Math; 1(2):99-107, 2012. [7] Gopalan M.A., Vidhyalakshmi S, Mallika S, Observations on hyperboloid of one sheet JMath; 2(3):221-226,2012. x 2 ? 2 y 2 ? z 2 ? 2, Bessel [8] Gopalan M.A., Vidhyalakshmi S, Usha Rani T.R., Mallika S, Integral points on the homogeneous cone 6z 2 ? 3y 2 ? 2x 2 ? 0, Impact J Sci Tech; 6(1):7-13, 2012. [9] Gopalan M.A., Vidhyalakshmi S, Sumathi G, Lattice points on the elliptic paraboloid Applied Mathematics;7(4): 379-385, 2012. z ? 9x 2 ? 4 y 2 , Advances in [10] Gopalan M.A., Vidhyalakshmi S, Usha Rani T.R.,Integral points on the non-homogeneous cone 2z 2 ? 4xy ? 8x ? 4z ? 0 , Global Journal of Mathematics and Mathematics sciences 2012;2(1):61-67. [11] Gopalan M.A., Vidhyalakshmi S, Lakshmi K, Lattice points on the elliptic paraboloid 16 y 2 ? 9z 2 ? 4x, Bessel J Math; [12] Python Object-Oriented Programming by Steven F.Lott and Dusty Phillips ,4th edition. [13] Effective Python by Brett Slatkin , 1st edition

Copyright

Copyright © 2023 K Hema, Ammineni Deepak Teja, Giri Kollati. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.