What does this research mean for the field?

Transformation techniques and factorization methods yield numerous non-zero distinct integer solutions to the non-homogeneous ternary nonic Diophantine equation 3(x2+y2)-5xy=(k2+11)z9. Novelty: ClaimNovelty.INCREMENTAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

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

March 21, 2026Open Access

A Collection of Integer Solutions to Non-homogeneous Ternary Nonic Diophantine Equation 3(x2+y2)-5xy=(k2+11) z9

Key Points

The aim is to find distinct non-zero integer solutions to a specific non-homogeneous ternary nonic equation.
Utilized transformation techniques to simplify the equation.
Employed factorization methods to derive solutions.
Focused on identifying distinct integer solutions for varying parameters.
Successfully found multiple non-zero distinct integer solutions.
Demonstrated the application of transformation and factorization methods on higher degree equations.

Abstract

Abstract This paper aims at determining non-zero distinct integer solutions to non-homogeneous ternary nonic Diophantine equation 3(x2+y2)-5xy=(k2+11) z9. Transformation techniques and factorization methods are utilized to obtain the same. We are able to solve the higher degree equation through the methods suggested above for obtaining plenty of non-zero distinct integer solutions.

A Collection of Integer Solutions to Non-homogeneous Ternary Nonic Diophantine Equation 3(x2+y2)-5xy=(k2+11) z9

Key Points

Abstract

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