What question did this study set out to answer?

The aim is to find non-zero distinct integer solutions to a specific ternary heptic Diophantine equation.

March 5, 2026Open Access

Patterns of Integer Solutions to Non-homogeneous Ternary Heptic Diophantine Equation X2+y2=(a2+b2) z2

Key Points

The aim is to find non-zero distinct integer solutions to a specific ternary heptic Diophantine equation.
Utilized transformation techniques to analyze the equations
Employed factorization methods for solution derivation
Identified several integer solutions to the heptic Diophantine equation
Demonstrated that distinct non-zero solutions exist

Abstract

Abstract This paper aims at determining non-zero distinct integer solutions to non-homogeneous ternary heptic Diophantine equation x 2 + y 2 = (a2+b2) z7. Transformation techniques and factorization methods are utilized to obtain the same.

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Cite This Study

Shanthi et al. (Tue,) studied this question.

synapsesocial.com/papers/69a91dedd6127c7a504c146e https://doi.org/https://doi.org/10.5281/zenodo.18845047

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