Many of the 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 ).
They discovered a variety of elegant and surprising
Theorems which are often easy to prove. In this article we shall
exhibit many of their results, and explore several extensions.
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