Supercongruences involving Domb numbers and binary quadratic forms
Number Theory
2021-12-24 v1
Abstract
In this paper, we prove two recently conjectured supercongruences (modulo , where is any prime greater than ) of Zhi-Hong Sun on truncated sums involving the Domb numbers. Our proofs involve a number of ingredients such as congruences involving specialized Bernoulli polynomials, harmonic numbers, binomial coefficients, and hypergeometric summations and transformations.
Keywords
Cite
@article{arxiv.2112.12732,
title = {Supercongruences involving Domb numbers and binary quadratic forms},
author = {Guo-Shuai Mao and Michael J. Schlosser},
journal= {arXiv preprint arXiv:2112.12732},
year = {2021}
}
Comments
17 pp