Fixed Points of Number Derivatives Modulo n

Authors

Franque Bains, Californaia State University, Los AngelesFollow

Abstract

A number derivative is a function that satisfies the Product Rule. In this paper, we find all solutions to the equation f (x)=x, where f is a number derivative on the ring of integers modulo an integer n. Thinking of number derivatives as analogues of the ordinary derivative from Calculus, we can think of this equation as a "differential equation" of sorts; solutions to it will then be rough analogues of exponential functions.

Author Bio

I am a math major at California State University, Los Angeles. This summer I was interested in learning about mathematics research and I approached Dr. Krebs about working on a project with him. I was very excited when Dr. Krebs allowed me to work with him. The research project was completed as a directed undergraduate study, where I worked one on one with Dr. Krebs this summer and fall. My goals are to study algebra and math education in a graduate program. My personal interests are singing, hiking, jogging and spending time with family and friends

Faculty Sponsor

Mike Krebs

Recommended Citation

Bains, Franque (2009) "Fixed Points of Number Derivatives Modulo n," Rose-Hulman Undergraduate Mathematics Journal: Vol. 10: Iss. 1, Article 1.
Available at: https://scholar.rose-hulman.edu/rhumj/vol10/iss1/1