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Download PDFOpen PDF in browserPrime Factorization and Diophantine Quintic Equations Insights, Challenges, and New DirectionsEasyChair Preprint 12823, version 27 pages•Date: March 29, 2024AbstractWhen 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. Keyphrases: Diophantine quintic equation, Prime number, algebraic methods Download PDFOpen PDF in browser |
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