Gaps in the sequence n2ϑ(mod1)
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 contr...
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| Format: | Article |
| Language: | English |
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Hindawi Limited
1987-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171287000164 |