1 / 1

Exploring the Number Derivative Function and its Applications

This paper delves into the number derivative n', a function based on prime factorization. It presents formulas, bounds, and relationships between n and n', analyzing its extension to rational numbers and solving related equations. The study by National Finalist Linda Westrick from Maggie L. Walker Governor’s School explores the function’s discontinuities and conditions for solutions.

jory
Download Presentation

Exploring the Number Derivative Function and its Applications

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Siemens Westinghouse CompetitionMath : Science : TechnologyNational Finalist • This paper explores the number derivative n', a function defined in terms of the prime factorization of a positive integer n. We find an explicit formula and bounds for the function and investigate how the prime factorizations of n and n' are related. We then extend the function (originally defined only on Z+U{0}) to the rational numbers and find all x in Q + such that x'=0. We prove that the number derivative is discontinuous over all Q+ . Finally, we analyze the equation x =áx for x in Q+ and x in Z+, and find the conditions under which this equation has a solution. • Name: Linda Westrick • High School: Maggie L. Walker Governor’s School for Government and International Studies, Richmond, VA • Mentor: Mr. Pavlo Pylyavskyy • Project Title: Investigations of the Number Derivative

More Related