{"title":"形式为(2t/k)的卢卡斯数","authors":"N. Irmak, L. Szalay","doi":"10.12697/ACUTM.2019.23.06","DOIUrl":null,"url":null,"abstract":"Let Lm denote the mth Lucas number. We show that the solutions to the diophantine equation (2t/k) = Lm, in non-negative integers t, k ≤ 2t−1, and m, are (t, k, m) = (1, 1, 0), (2, 1, 3), and (a, 0, 1) with non-negative integers a.","PeriodicalId":42426,"journal":{"name":"Acta et Commentationes Universitatis Tartuensis de Mathematica","volume":"144 1 1","pages":""},"PeriodicalIF":0.3000,"publicationDate":"2019-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Lucas numbers of the form (2t/k)\",\"authors\":\"N. Irmak, L. Szalay\",\"doi\":\"10.12697/ACUTM.2019.23.06\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let Lm denote the mth Lucas number. We show that the solutions to the diophantine equation (2t/k) = Lm, in non-negative integers t, k ≤ 2t−1, and m, are (t, k, m) = (1, 1, 0), (2, 1, 3), and (a, 0, 1) with non-negative integers a.\",\"PeriodicalId\":42426,\"journal\":{\"name\":\"Acta et Commentationes Universitatis Tartuensis de Mathematica\",\"volume\":\"144 1 1\",\"pages\":\"\"},\"PeriodicalIF\":0.3000,\"publicationDate\":\"2019-08-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Acta et Commentationes Universitatis Tartuensis de Mathematica\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.12697/ACUTM.2019.23.06\",\"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":"Acta et Commentationes Universitatis Tartuensis de Mathematica","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.12697/ACUTM.2019.23.06","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
摘要
设Lm表示第m个Lucas数。我们证明了在非负整数t, k≤2t - 1和m下，diophantine方程(2t/k) = Lm的解为(t, k, m) =(1,1,0)，(2,1,3)和(a, 0,1)，且非负整数为a。
Let Lm denote the mth Lucas number. We show that the solutions to the diophantine equation (2t/k) = Lm, in non-negative integers t, k ≤ 2t−1, and m, are (t, k, m) = (1, 1, 0), (2, 1, 3), and (a, 0, 1) with non-negative integers a.
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