Prime Factorization and Diophantine Quintic Equations Insights, Challenges, and New Directions

Published: 28 March 2024| Version 1 | DOI: 10.17632/dhk6bsbmcp.1
Contributor:
budee zaman

Description

When discussing the Diophantine quintic equation $p(a^5 + b^5) = q(c^5 + d^5)$ where p is a prime and q is an integer, there is a clear gap between the mathematical literature and online forums. Because of the intrinsic complexity of parameterizing fifth-degree equations, this equation re- mains largely unexplored. In this work, we approach this quintic problem through algebraic methods with the goal of providing numerical solutions that illuminate its properties and behaviors.Our research uncovers in- triguing patterns and connections that shed light on the enigmatic nature of Diophantine quintic equations in this particular form.

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The mathematical community has always been intrigued and curious about Diophantine equations. Diaphanous of Alexandria, a Greek mathematician, is the inspiration behind their name. The goal of these questions is to find integer solutions to polynomial equations with several variables.

Institutions

Punjab Group of Colleges

Categories

Number Theory

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