On a relationship between the convergents of the nearest integer and regular continued fractions

Author:
William W. Adams

Journal:
Math. Comp. **33** (1979), 1321-1331

MSC:
Primary 10K10; Secondary 10K15

DOI:
https://doi.org/10.1090/S0025-5718-1979-0537978-9

MathSciNet review:
537978

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Abstract: In this paper we derive a relation concerning the speed of convergence of the nearest integer and regular continued fractions. If , denote the convergents of the nearest integer and regular continued fractions of an irrational number , then for all *n* there is a such that . It is shown that

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DOI:
https://doi.org/10.1090/S0025-5718-1979-0537978-9

Article copyright:
© Copyright 1979
American Mathematical Society