Integral Solutions of the Ternary Cubic Equation

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

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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.