The Arithmetic Derivative: How to Differentiate a Number
Item
- Description
- David F. Putnam Science Center, Room 102
- The arithmetic derivative of a natural number n, denoted n', is defined as follows: If n is prime then n'=1 and for natural numbers a and b, then (ab)'=ab'+ba'. This rule for (ab)' has the same form as the Leibniz Rule in Calculus. This talk will explore some basic properties of the arithmetic derivative with an emphasis on those that have analogs in Calculus. The definition will then be extended to apply to integers and rational numbers. Connections between the arithmetic derivative and two famous unsolved problems in number theory, Goldbach's Conjecture and the Twin Primes Conjecture, will be included.
- Vincent Ferlini
- Contributor
- Keene State College
- Creator
- Heather M. Paight
- Date
- 2016-04-09
- Identifier
- https://commons.keene.edu/s/KSCArchive/item/21029
- Language
- en_US
- Subject
- Mathematics
- Type
- Presentation
- Rights
- http://rightsstatements.org/vocab/InC/1.0/
- Site pages
- School of Sciences and Social Sciences
Position: 2815 (26 views)