Manjil P. Saikia, Abhishek Sarma, Pranjal Talukdar
{"title":"Ramanujan-type congruences for partition k-tuples with 5-cores","authors":"Manjil P. Saikia, Abhishek Sarma, Pranjal Talukdar","doi":"10.1007/s13226-024-00566-8","DOIUrl":null,"url":null,"abstract":"<p>We prove several Ramanujan-type congruences modulo powers of 5 for partition <i>k</i>-tuples with 5-cores, for <span>\\(k=2, 3, 4\\)</span>. We also prove some new infinite families of congruences modulo powers of primes for <i>k</i>-tuples with <i>p</i>-cores, where <i>p</i> is a prime.</p>","PeriodicalId":501427,"journal":{"name":"Indian Journal of Pure and Applied Mathematics","volume":"25 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Indian Journal of Pure and Applied Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s13226-024-00566-8","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
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Abstract
We prove several Ramanujan-type congruences modulo powers of 5 for partition k-tuples with 5-cores, for \(k=2, 3, 4\). We also prove some new infinite families of congruences modulo powers of primes for k-tuples with p-cores, where p is a prime.
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