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# Talk: On the q-binomial coefficients and binomial congruences (Illinois)

On the q-binomial coefficients and binomial congruences (Illinois)

Date: 2012/11/15
Occasion: q-Series Seminar
Place: University of Illinois at Urbana-Champaign

## Abstract

In the first part of this talk, the q-binomial coefficients are introduced in a variety of different ways in order to demonstrate that they are a very natural and beautiful generalization of the usual binomial coefficients. Having thus established that they are interesting objects in their own right, we consider classical congruences for binomial coefficients with the objective of extending them to the q-world. Our focus here is on Ljunggren's congruence, which states that $$\binom{ap}{bp}$$ is congruent to $$\binom{a}{b}$$ modulo $$p^3$$.