The Arithmetic Properties of Binomial Coefficients
Andrew Granville
Department of Mathematics
University of Georgia
Athens, GA
Abstract:

Many great mathematicians of the nineteenth century considered
problems involving binomial coefficients modulo a prime power
(for instance Babbage, Cauchy, Cayley, Gauss, Hensel, Hermite,
Kummer, Legendre, Lucas and Stickelberger  see Dickson).
They discovered a variety of elegant and surprising Theorems
which are often easy to prove. In this article we shall exhibit most
of these results, and extend them in a variety of ways.