A Layer-Based Framework for Differences of Powers
Year: 2026
Type: article
Abstract: This research note presents a layer-based framework for studying differences of powers. It defines the layer operator as L_n(k) = k^n - (k-1)^n and develops its telescoping, polynomial, finite-difference, recurrence, combinatorial, and arithmetic interpretations. Classical identities and standard finite-difference results are identified explicitly, while arithmetic divisibility, greatest-common-divisor, residue-class, and higher-difference questions are presented as directions for further research. The note is intended as a structured framework for theorem development rather than a claim of a completed new foundational classification theorem.
Author: Mamdouh, Adam
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7212438707
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