Ijraset Journal For Research in Applied Science and Engineering Technology

Abstract

The non-homogenous cubic equation with three unknowns represented by the Diophantine equation 3(x^2+y^2)-4(xy)+2(x+y+1)=522z^3 is analyzed for its patterns of stringfy integral solutions. A few interesting properties among the solutions and some special polygonal numbers are presented.

Introduction

Conclusion

CONCLUSION In this paper, we have presented five different patterns of non-zero distinct integer solutions of the non-homogeneous cone given by 3(x^2+y^2)-4(xy)+2(x+y+1)=522z^3 To conclude, one may search for other patterns of non-zero integer distinct solutions and their corresponding properties for other choices of cubic Diophantine equations.

References

[1] Dickson L.E., “History of the theory of numbers”, Chelsia Publishing Co., Sol II, New York, 1952 [2] Carmichael R.D., “The Theory of Numbers and Diophantine Analysis”, Dover Publications, New York, 1959 [3] Mordell L .J., “Diophantine Equations”, Academic Press, London 1969 [4] Telang S. G., “Number Theory”, Tata Mc Graw-Hill Publishing Company, New Delhi 1996 [5] Janaki G, Saranya C, “Observations on Ternary Quadratic Diophantine Equation ”, International Journal of Innovative Research and science, Engineering and Technology, volume 5, Issue 2, February 2016 [6] Janaki G, Saranya C, “Integral Solutions of the Ternary Cubic Equation ”, International Research Journal of Engineering and Technology vol-4, Issue 3, Pg. No: 665-669, March 201 [7] Janaki G, Radha R, “On Ternary Quadratic Diophantine Equation ”, International Journal for Research in Applied Science and Engineering Technology”, vol 6, Issue I, Pg. No: 2656-2660, January 2018 [8] Janaki G, Gowri Shankari A, “Properties of the Ternary Cubic Equation ”, International Journal for Research in Applied Science and Engineering Technology, vol 10, Issue III,Pg.No: 231-234, August 2022

Copyright

Copyright © 2023 G. Janaki, J. Rahini. 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.