Number Theory

    

Extended Diophantine Equation

Authors: Dinh Van Tien

This paper presents a comprehensive overview of extended Diophantine equations—high-degree equations that admit infinitely many solution sets, with each set comprising infinitely many elements. We focus on the effective application of the formula: ab = k(a+b) + c, where a, b, k, and c are integers, to transform complex equations into symmetric forms. This transformation facilitates the derivation of polynomial expansions and enables the systematic construction of solution sets with distinct and primitive elements.

Comments: 54 Pages.

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[v1] 2025-03-25 02:27:24

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