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标题：Gaps in the sequence <mml:math alttext="$n^2 \vartheta \left( {\bmod 1} \right)$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mi>n</mml:mi><mml:mn>2</mml:mn></mml:msup><mml:mi>ϑ</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mo>mod</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math>
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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
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 I0,I1,…,IN be the intervals resulting from the partition of [0,1] by the points {k2ϑ}, 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 {nϑ}, where T(N)≤3.