文章基本信息

标题：Gaps in the sequence n2ϑ(mod1)
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作者：Vladimir Drobot
期刊名称：International Journal of Mathematics and Mathematical Sciences
印刷版ISSN：0161-1712
电子版ISSN：1687-0425
出版年度：1987
卷号：10
期号：1
页码：131-134
DOI：10.1155/S0161171287000164
出版社：Hindawi Publishing Corporation
摘要：
Let ϑ be an irrational number and let { t } denote the fractional part of t . For each N let I 0 , I 1 , … , I N be the intervals resulting from the partition of [ 0 , 1 ] by the points { k 2 ϑ } , k = 1 , 2 , … , N . Let T ( N ) be the number of distinct lengths these intervals can assume. It is shown that T ( N ) → ∞ . This is in contrast to the case of the sequence { n ϑ } , where T ( N ) ≤ 3 .