{"title":"On the exponential Diophantine equation (4m²+1)ˣ + (21m²-1)ʸ = (5m)ᶻ","authors":"N. Terai","doi":"10.33039/ami.2020.01.003","DOIUrl":null,"url":null,"abstract":"Let m be a positive integer. Then we show that the exponential Diophantine equation (4m+1)+(21m−1) = (5m) has only the positive integer solution (x, y, z) = (1, 1, 2) under some conditions. The proof is based on elementary methods and Baker’s method.","PeriodicalId":43454,"journal":{"name":"Annales Mathematicae et Informaticae","volume":null,"pages":null},"PeriodicalIF":0.3000,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"11","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annales Mathematicae et Informaticae","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.33039/ami.2020.01.003","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: 11
Abstract
Let m be a positive integer. Then we show that the exponential Diophantine equation (4m+1)+(21m−1) = (5m) has only the positive integer solution (x, y, z) = (1, 1, 2) under some conditions. The proof is based on elementary methods and Baker’s method.
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