Seminar Details
Lucas Congruences Modulo p2
- Start Date: November 4, 2021
- Event Start Time: 5:00 PM
- Event End Time: 6:00 PM
- Seminar Series: Experimental Math Seminar
- Presenter(s): Eric Rowland - Hofstra University
- Event Location: Online Event
- Event Additional Info: <p>Presented Via Zoom: <a href="https://rutgers.zoom.us/j/94346444480">https://rutgers.zoom.us/j/94346444480</a></p> <p>Password: 6564120420</p> <p>For further information see: <a href="https://sites.math.rutgers.edu/~zeilberg/expmath/">https://sites.math.rutgers.edu/~zeilberg/expmath/</a></p>
- Presentation Type: Stand Alone Presentation
- Abstract:
In the 1870s, Lucas obtained a beautiful formula for binomial coefficients modulo p. Namely, Binomial[n, m] is congruent modulo p to the product of the binomial coefficients whose arguments are the base-p digits of n and m, taken pairwise. Variations and generalizations of this formula have been actively investigated since. In particular, for which n and m does Lucas' congruence hold not just modulo p but modulo p2? The answer is related to some hidden rotational symmetry in Pascal's triangle. A similar result holds for the Apéry numbers, which Gessel showed satisfy a Lucas congruence in 1982.
Link to video: https://vimeo.com/644157702