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