{"title":"指数丢番图方程(4m²+1)μ k + (21m²-1)↓= (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":"{\"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}","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
摘要
设m为正整数。然后证明了指数型丢芬图方程(4m+1)+(21m−1)= (5m)在某些条件下只有正整数解(x, y, z) =(1,1,2)。证明是基于初等方法和贝克方法。
On the exponential Diophantine equation (4m²+1)ˣ + (21m²-1)ʸ = (5m)ᶻ
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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