{"title":"由三个重复数字组成的平衡数","authors":"F. Erduvan, R. Keskin","doi":"10.15330/cmp.16.1.148-157","DOIUrl":null,"url":null,"abstract":"In this study, it is shown that the only balancing numbers which are concatenations of three repdigits are $204$ and $1189$. The proof depends on lower bounds for linear forms and some tools from Diophantine approximation.","PeriodicalId":42912,"journal":{"name":"Carpathian Mathematical Publications","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2024-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Збалансовані числа, які є конкатенацією трьох репдиджитів\",\"authors\":\"F. Erduvan, R. Keskin\",\"doi\":\"10.15330/cmp.16.1.148-157\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this study, it is shown that the only balancing numbers which are concatenations of three repdigits are $204$ and $1189$. The proof depends on lower bounds for linear forms and some tools from Diophantine approximation.\",\"PeriodicalId\":42912,\"journal\":{\"name\":\"Carpathian Mathematical Publications\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2024-06-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Carpathian Mathematical Publications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.15330/cmp.16.1.148-157\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Carpathian Mathematical Publications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.15330/cmp.16.1.148-157","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
Збалансовані числа, які є конкатенацією трьох репдиджитів
In this study, it is shown that the only balancing numbers which are concatenations of three repdigits are $204$ and $1189$. The proof depends on lower bounds for linear forms and some tools from Diophantine approximation.
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