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On Integers n Relatively Prime to [ αn ]
G. L. Watson
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Source: Crossref
Published: Jan 1, 1953
DOI: 10.4153/cjm-1953-050-9
Open original source ↗Source abstract
The object of this paper is to consider a problem suggested by Dr. K. F. Roth, on the distribution of integers n that are relatively prime to the integral part of an, a being a fixed real number. He conjectured that the number of positive integers up to x with this property is asymptotic to (or in other words that they have the density ), for irrational a. I prove this and rather more in the following
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