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Abstract:

Binomial Coefficients have many remarkable arithmetic properties. We hope to maintain an enduring website which will serve as an introduction to many of those properties as well as a survey of much of what is already known. This article reflects that survey at the time of publication; however by the time the reader views this, there may have been a significant expansion of the on-line `dynamic survey' at http://www.math.uga.edu:80/~andrew/Binomial/index.html

At present our main focus is on binomial coefficients modulo given prime powers. We will discuss many results, both old and new. We have collected together some of the diverse directions taken in this subject, for example discussing connections with cellular automata, Fermat's Last Theorem and the prime recognition problem, providing proofs where it seems appropriate.