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Talk: A q-analog of Ljunggren's binomial congruence (Illinois)

A q-analog of Ljunggren's binomial congruence (Illinois)

Date: 2012/10/13
Occasion: Midwest Number Theory Conference for Graduate Students and Recent PhDs IX
Place: University of Illinois at Urbana-Champaign

Abstract

Ljunggren's congruence states that $$\binom{ap}{bp}$$ is congruent to $$\binom{a}{b}$$ modulo $$p^3$$. The goal of this talk is to extend this congruence into the q-world. To this end, the q-binomial coefficients are reviewed and characterized in a variety of ways.