Digital representations using the greatest integer function

Author:
Bruce Reznick

Journal:
Trans. Amer. Math. Soc. **312** (1989), 355-375

MSC:
Primary 11A63

DOI:
https://doi.org/10.1090/S0002-9947-1989-0954602-4

MathSciNet review:
954602

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Abstract | References | Similar Articles | Additional Information

Abstract: Let denote the set of all integers which can be expressed in the form , with , where is an integer and is real, and let denote the set of so that . We show that , where and for . If we show that , the complement of , is infinite, and discuss the density of when . For and a particular quadratic irrational , we describe explicitly and show that is of order , where .

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DOI:
https://doi.org/10.1090/S0002-9947-1989-0954602-4

Article copyright:
© Copyright 1989
American Mathematical Society