{"title":"Supercongruences involving Domb numbers and binary quadratic forms.","authors":"Guo-Shuai Mao, Michael J Schlosser","doi":"10.1007/s13398-023-01509-4","DOIUrl":null,"url":null,"abstract":"<p><p>In this paper, we prove two recently conjectured supercongruences (modulo <math><msup><mi>p</mi><mn>3</mn></msup></math>, where <i>p</i> 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.</p>","PeriodicalId":54471,"journal":{"name":"Revista De La Real Academia De Ciencias Exactas Fisicas Y Naturales Serie A-Matematicas","volume":"118 1","pages":"11"},"PeriodicalIF":1.8000,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10547664/pdf/","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Revista De La Real Academia De Ciencias Exactas Fisicas Y Naturales Serie A-Matematicas","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s13398-023-01509-4","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2023/10/3 0:00:00","PubModel":"Epub","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
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Abstract
In this paper, we prove two recently conjectured supercongruences (modulo , 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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