Area of Study
Science and Mathematics
The binomial coefficients are interestingly always integral. However, when you generalize the binomial coefficients to any class of function, this is not always the case. Multiplicative functions satisfy the properties: f(ab) = f(a)f(b) when a and b are relatively prime, and f(1) = 1. Tom Edgar of Pacific Lutheran University and Michael Spivey of the University of Puget Sound developed a Corollary that determines which values of n and m will always have integral generalized binomial coefficients for all multiplicative functions. The purpose of this research was to determine as many patterns within this corollary as possible as well as patterns with the generalized binomial coefficients of specific non-divisible,multiplicative functions.
Chen, Imanuel, "Integral Generalized Binomial Coefficients of Multiplicative Functions" (2015). Summer Research. 238.
University of Puget Sound