Supercongruences involving Domb numbers and binary quadratic forms

In this paper, we prove two recently conjectured supercongruences (modulo [Formula: see text] , where p is any prime greater than 3) of Zhi-Hong Sun on truncated sums involving the Domb numbers. Our proofs involve a number of ingredients such as congruences involving specialized Bernoulli polynomial...

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Detalles Bibliográficos
Autores principales: Mao, Guo-Shuai, Schlosser, Michael J.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2023
Materias:
Original Paper
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10547664/
https://www.ncbi.nlm.nih.gov/pubmed/37800097
http://dx.doi.org/10.1007/s13398-023-01509-4
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author Mao, Guo-Shuai
Schlosser, Michael J.
author_facet Mao, Guo-Shuai
Schlosser, Michael J.
author_sort Mao, Guo-Shuai
collection PubMed
description In this paper, we prove two recently conjectured supercongruences (modulo [Formula: see text] , where p is any prime greater than 3) 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.
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spelling pubmed-105476642023-10-05 Supercongruences involving Domb numbers and binary quadratic forms Mao, Guo-Shuai Schlosser, Michael J. Rev R Acad Cienc Exactas Fis Nat A Mat Original Paper In this paper, we prove two recently conjectured supercongruences (modulo [Formula: see text] , where p is any prime greater than 3) 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. Springer International Publishing 2023-10-03 2024 /pmc/articles/PMC10547664/ /pubmed/37800097 http://dx.doi.org/10.1007/s13398-023-01509-4 Text en © The Author(s) 2023 https://creativecommons.org/licenses/by/4.0/Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) .
spellingShingle Original Paper
Mao, Guo-Shuai
Schlosser, Michael J.
Supercongruences involving Domb numbers and binary quadratic forms
title Supercongruences involving Domb numbers and binary quadratic forms
title_full Supercongruences involving Domb numbers and binary quadratic forms
title_fullStr Supercongruences involving Domb numbers and binary quadratic forms
title_full_unstemmed Supercongruences involving Domb numbers and binary quadratic forms
title_short Supercongruences involving Domb numbers and binary quadratic forms
title_sort supercongruences involving domb numbers and binary quadratic forms
topic Original Paper
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10547664/
https://www.ncbi.nlm.nih.gov/pubmed/37800097
http://dx.doi.org/10.1007/s13398-023-01509-4
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