Obtaining New Dividing Formulas n|Q(n) From the Known Ones
Bau-Sen Du
TL;DR
This paper introduces methods based on discrete dynamical systems to generate new functions Q(n) that satisfy divisibility formulas n|Q(n), expanding the toolkit for understanding divisibility properties.
Contribution
It presents novel theorems that provide systematic ways to derive new divisibility formulas from existing functions using dynamical systems theory.
Findings
New methods for generating divisibility formulas
Theorems 1, 2, and 3 for constructing functions Q(n)
Extensions of known divisibility properties
Abstract
In this note, we present a few methods (Theorems 1, 2, and 3) from discrete dynamical systems theory of obtaining new functions Q(n) from the known ones so that the dividing formulas n|Q(n) hold.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Chaos control and synchronization · Advanced Differential Equations and Dynamical Systems