Properties of the Ternary Cubic Equation 5x2-3y2=z3

Abstract

To identify its different integral non-zero solutions, the ternary cubic equation is taken into consideration. Different integral solution patterns to the ternary cubic equation under consideration are obtained in each pattern by using the linear transformation and the method of factorization; interesting relationships between the solutions and some polygonal numbers, such as pyramidal and central pyramidal numbers, are also displayed.

Introduction

Conclusion

Three unique patterns of non-zero distinct integer solutions to the given non-homogeneous problem are shown in this paper. For various options of cubic Diophantine equations, additional patterns of non-zero integer unique solutions and their corresponding characteristics may be found.

References

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Copyright

Copyright © 2022 G. Janaki, A. Gowri Shankari. 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.