Supercongruences for sums involving Domb numbers

Supercongruences Involving Multiple Harmonic Sums and Bernoulli Numbers

In this paper, we study some supercongruences involving multiple harmonic sums by using Bernoulli numbers. Our main theorem generalizes previous results by many different authors and confirms a conjecture by the authors and their collaborators. In the proof, we will need not only the ordinary multiple harmonic sums in which the indices are ordered, but also some variant forms in which the indic...

Supercongruences for Apéry-like Numbers

It is known that the numbers which occur in Apéry’s proof of the irrationality of ζ(2) have many interesting congruence properties while the associated generating function satisfies a second order differential equation. We prove supercongruences for a generalization of numbers which arise in Beukers’ and Zagier’s study of integral solutions of Apéry-like differential equations.

A Supercongruence for Generalized Domb Numbers

Using techniques due to Coster, we prove a supercongruence for a generalization of the Domb numbers. This extends a recent result of Chan, Cooper and Sica and confirms a conjectural supercongruence for numbers which are coefficients in one of Zagier’s seven “sporadic” solutions to second order Apéry-like differential equations.

Supercongruences for the Catalan-Larcombe-French numbers

In this short note, we develop the Stienstra-Beukers theory of supercongruences in the setting of the Catalan-Larcombe-French sequence. We also give some applications to other sequences. AMS Subject Classification: 11B83, 11B65, 11F30, 33E05

Some New Finite Sums Involving Generalized Fibonacci And Lucas Numbers