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A Glimpse on the Non-homogeneous Quaternary Octic Surface x3+y3=2(a2+3b2) zw7 | Synapse

March 18, 2026Open Access

A Glimpse on the Non-homogeneous Quaternary Octic Surface x3+y3=2(a2+3b2) zw7

Key Points

The paper aims to derive non-zero distinct integer solutions for a specific non-homogeneous quaternary octic equation.
Utilized substitution technique for solving equations.
Employed factorization method to derive solutions.
Focused on the equation x^3 + y^3 = (a^2 + 3b^2) zw^7.
Successfully obtained multiple non-zero distinct integer solutions.
Demonstrated effectiveness of the substitution and factorization methods.

Abstract

Abstract The main aim of this paper is to illustrate the process of obtaining non-zero distinct integer solutions to the non-homogeneous quaternary octic equation represented by x3+y3=(a2+3b2) zw7 Substitution technique and factorization method are utilized to obtain the same. We are able to solve the given octic equation through the methods suggested above for obtaining plenty of non-zero distinct integer solutions.

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Authors

N

N. Thiruniraiselvi

J

J. Shanthi

M

M.A. Gopalan

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Institutions

Anna University, Chennai

Bharathidasan University

Sri Ramakrishna Institute of Paramedical Sciences

References and Citations

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Cite this study

Thiruniraiselvi et al. (Mon,) studied this question.

www.synapsesocial.com/papers/69ba434a4e9516ffd37a4618 — DOI: https://doi.org/10.5281/zenodo.19044892