Seminars & Colloquia Calendar

Download as iCal file

Experimental Mathematics Seminar

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:
password: The 20th Catalan number, alias (40)!/(20!*21!), alias 6564120420

Special Note to All Travelers

Directions: map and driving directions. If you need information on public transportation, you may want to check the New Jersey Transit page.

Unfortunately, cancellations do occur from time to time. Feel free to call our department: 848-445-6969 before embarking on your journey. Thank you.