March 14, 2024International Journal for Research in Applied Science and Engineering TechnologyOpen Access

On Integer Solutions of the Ternary Bi-Quadratic Diophantine Equation 14(x^2+y^2)-24xy=17z^4

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The investigation identifies integral solutions to the diophantine equation through various patterns.
Up to four distinct solution patterns are explored to understand the relationships between the solutions.
Assessment of unique polygonal numbers contributes to the understanding of the equation's properties and integrality issues. The findings suggest deeper connections among distinct solutions, defining a framework for future studies in number theory.

Implication

Analysis reveals distinct integral solutions to a bi-quadratic Diophantine equation, highlighting connections among solutions.

Abstract

This analysis is discussed on the non-trivial distinct integral solution to the ternary bi-quadratic diophantine equation 4 ) 24 17 2 2 14(x  y  xy  z , in four dissimilar patterns. Few connections between the solutions are obtained and also unique polygonal numbers are described

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Cite This Study

Janaki et al. (2024) studied this question.

synapsesocial.com/papers/68e741feb6db6435876baf88 https://doi.org/10.22214/ijraset.2024.58971

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Implication

Analysis reveals distinct integral solutions to a bi-quadratic Diophantine equation, highlighting connections among solutions.

On Integer Solutions of the Ternary Bi-Quadratic Diophantine Equation 14(x^2+y^2)-24xy=17z^4

Key Points

Implication

Abstract

Discussion

Cite This Study

On Integer Solutions of the Ternary Bi-Quadratic Diophantine Equation 14(x^2+y^2)-24xy=17z^4

Key Points

Implication

Abstract

Discussion

Cite This Study

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