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

Budee U Zaman

doi:10.20944/preprints202403.1718.v1

Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Version 1 : Received: 27 March 2024 / Approved: 28 March 2024 / Online: 28 March 2024 (09:35:31 CET)

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.

algebraic methods,quintic problem,Diophantine equation ,prime number

Computer Science and Mathematics, Algebra and Number Theory

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

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