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.