{"title":"Generalized Mersenne numbers of the form cx²","authors":"Azizul Hoque","doi":"10.33039/ami.2022.05.002","DOIUrl":null,"url":null,"abstract":"Generalized Mersenne numbers are defined as 𝑀 𝑝,𝑛 = 𝑝 𝑛 − 𝑝 +1 , where 𝑝 is a prime and 𝑛 is a positive integer. Here, we prove that for each pair ( 𝑐, 𝑝 ) with 𝑐 ≥ 1 an integer, there is at most one 𝑀 𝑝,𝑛 of the form 𝑐𝑥 2 with a few exceptions.","PeriodicalId":43454,"journal":{"name":"Annales Mathematicae et Informaticae","volume":"32 1","pages":""},"PeriodicalIF":0.3000,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annales Mathematicae et Informaticae","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.33039/ami.2022.05.002","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
Generalized Mersenne numbers are defined as 𝑀 𝑝,𝑛 = 𝑝 𝑛 − 𝑝 +1 , where 𝑝 is a prime and 𝑛 is a positive integer. Here, we prove that for each pair ( 𝑐, 𝑝 ) with 𝑐 ≥ 1 an integer, there is at most one 𝑀 𝑝,𝑛 of the form 𝑐𝑥 2 with a few exceptions.
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