{"title":"关于Ramanujan-Nagell型丢番图方程 \\(Dx^2+k^n=B\\)","authors":"Zhong-Can Zhang, A. Togbé","doi":"10.3336/gm.56.2.04","DOIUrl":null,"url":null,"abstract":"In this paper, we prove that the Ramanujan-Nagell type Diophantine equation \\(Dx^2+k^n=B\\) has at most three nonnegative integer solutions \\((x, n)\\) for \\(k\\) a prime and \\(B, D\\) positive integers.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the Ramanujan-Nagell type Diophantine equation \\\\(Dx^2+k^n=B\\\\)\",\"authors\":\"Zhong-Can Zhang, A. Togbé\",\"doi\":\"10.3336/gm.56.2.04\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we prove that the Ramanujan-Nagell type Diophantine equation \\\\(Dx^2+k^n=B\\\\) has at most three nonnegative integer solutions \\\\((x, n)\\\\) for \\\\(k\\\\) a prime and \\\\(B, D\\\\) positive integers.\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2021-12-23\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.3336/gm.56.2.04\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.3336/gm.56.2.04","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
On the Ramanujan-Nagell type Diophantine equation \(Dx^2+k^n=B\)
In this paper, we prove that the Ramanujan-Nagell type Diophantine equation \(Dx^2+k^n=B\) has at most three nonnegative integer solutions \((x, n)\) for \(k\) a prime and \(B, D\) positive integers.
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