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Recurrences in multidimensional arithmetic sequences

Published online by Cambridge University Press:  24 October 2008

S. Hemmer  and
P. C. Hemmer
S. Hemmer
Affiliation:
Blussuvoll skole and University of Trondheim
P. C. Hemmer
Affiliation:
Blussuvoll skole and University of Trondheim
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Extract

Let unity and the irrational components ri of a d-dimensional vector r be linearly independent, and consider the integers n for which

where {x} denotes the fractional part of x. It is a trivial restriction to assume that ri and φi lie between 0 and 1. This note is concerned with the question: what are the gaps between the successive n?

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 93 , Issue 3 , May 1983 , pp. 393 - 396
Copyright
Copyright © Cambridge Philosophical Society 1983

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References

REFERENCES

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(4)Weyl, H.Über die Gleichverteilung von Zahlen mod. Eins. Math. Ann. 77 (1916), 313–352.CrossRefGoogle Scholar