Friday, April 17
Fixed Points of Number Derivatives Modulo n
Franque Bains, MARC U*STAR Scholar
Do you remember the product rule from calculus? The product rule allows you to find the derivative of a product of two familiar functions and looks like this: D(fg) = f D(g) + g D(f). Similarly, a number derivative is a mapping that satisfies the product rule. In other words, f is a number derivative if f(nm) = n f(m) + m f(n). Here, though, n and m are not functions; they are integers modulo n. In this research project, the objective is to find formulas that derive all fixed points of a number derivative on the set Zn of integers modulo n. (x is a fixed point of the function f if and only if f(x) = x.) This talk will cover the results of this research project. C. Emmons, M. Krebs, A. Shaheen. How to differentiate an integer mod n.