{"title":"以m为模的平衡数序列的均匀分布","authors":"P. Ray, Bijan Kumar Patel","doi":"10.1515/udt-2016-0002","DOIUrl":null,"url":null,"abstract":"Abstract The balancing numbers and the balancers were introduced by Behera et al. in the year 1999, which were obtained from a simple diophantine equation. The goal of this paper is to investigate the moduli for which all the residues appear with equal frequency with a single period in the sequence of balancing numbers. Also, it is claimed that, the balancing numbers are uniformly distributed modulo 2, and this holds for all other powers of 2 as well. Further, it is shown that the balancing numbers are not uniformly distributed over odd primes.","PeriodicalId":23390,"journal":{"name":"Uniform distribution theory","volume":"44 1","pages":"15 - 21"},"PeriodicalIF":0.0000,"publicationDate":"2016-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":"{\"title\":\"Uniform Distribution of the Sequence of Balancing Numbers Modulo m\",\"authors\":\"P. Ray, Bijan Kumar Patel\",\"doi\":\"10.1515/udt-2016-0002\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract The balancing numbers and the balancers were introduced by Behera et al. in the year 1999, which were obtained from a simple diophantine equation. The goal of this paper is to investigate the moduli for which all the residues appear with equal frequency with a single period in the sequence of balancing numbers. Also, it is claimed that, the balancing numbers are uniformly distributed modulo 2, and this holds for all other powers of 2 as well. Further, it is shown that the balancing numbers are not uniformly distributed over odd primes.\",\"PeriodicalId\":23390,\"journal\":{\"name\":\"Uniform distribution theory\",\"volume\":\"44 1\",\"pages\":\"15 - 21\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2016-06-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"4\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Uniform distribution theory\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1515/udt-2016-0002\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Uniform distribution theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1515/udt-2016-0002","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Uniform Distribution of the Sequence of Balancing Numbers Modulo m
Abstract The balancing numbers and the balancers were introduced by Behera et al. in the year 1999, which were obtained from a simple diophantine equation. The goal of this paper is to investigate the moduli for which all the residues appear with equal frequency with a single period in the sequence of balancing numbers. Also, it is claimed that, the balancing numbers are uniformly distributed modulo 2, and this holds for all other powers of 2 as well. Further, it is shown that the balancing numbers are not uniformly distributed over odd primes.
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