Seminars & Colloquia Calendar
Lucas congruences modulo p2
Eric Rowland, Hofstra University
Location: Zoom
Date & time: Thursday, 04 November 2021 at 5:00PM - 6:00PM
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
Zoom link: https://rutgers.zoom.us/j/94346444480
password: The 20th Catalan number, alias (40)!/(20!*21!), alias 6564120420
password: The 20th Catalan number, alias (40)!/(20!*21!), alias 6564120420
