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

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


Punjab Group of Colleges


Number Theory