Book

This book presents a deterministic algorithmic approach to partitioning arithmetic progressions into subsets with equal sums. At the heart of the work is an original constructive procedure designed to systematically organize the elements of an arithmetic progression into equal-sum groups. The method addresses both even and odd numbers of elements, providing structured constructions and mathematical reasoning for each case. Moving from foundational concepts to algorithmic development, the book introduces the underlying principles, formal definitions, mathematical formulations, and step-by-step procedures that govern the partitioning process. It examines the structure of the resulting subsets, explains the construction mechanisms, and presents examples that illustrate how the algorithm operates. Particular attention is given to the deterministic nature of the method, its systematic construction strategy, and the mathematical properties of the resulting partitions. Beyond the core algorithm, the book discusses potential applications in balanced allocation and other computational settings involving structured numerical data, while distinguishing the demonstrated mathematical results from broader application possibilities. Combining mathematical constructions with algorithmic analysis, this work offers researchers, computer scientists, and readers interested in discrete structures and computational algorithms a detailed study of a constructive approach to equal-sum partitioning.