Geometric Loci Arising from Rational Prodsum Sets and Their Recursive GenerationGenerate Audio Overview

This collection of papers investigates sets of numbers where the sum of the elements is equivalent to their product, termed "prodsum" sets. Initial inquiries establish the foundational properties of finite prodsum sets within the rational number system, commencing with an analysis of integer solutions and subsequently extending to encompass the wider scope of rational solutions. Further exploration introduces recursive methodologies for the generation of these distinctive sets, culminating in the derivation of a generalized formula that defines an element based on its predecessors. The analysis of dual and tri-element recursive prodsum sets reveals underlying principles and patterns governing their construction. Additionally, the research examines the geometric loci generated by a specific complex rational function and its relationship to these recursive prodsum characteristics, thereby connecting concepts from number theory and complex analysis.