Abstract
For any prime p, we establish congruences modulo pn+1 for the difference of the pn+1 th and pn th Motzkin numbers and determine the p-adic order of the difference. The results confirm recent conjectures on the order. The applied techniques involve the use of congruences for the differences of certain Catalan numbers and binomial coefficients, congruential identities for sums of Catalan numbers, central binomial and trinomial coefficients, infinite incongruent disjoint covering systems and the solution of congruential recurrences.
Full Text
Published Version
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call