A theorem on the -adic representation of positive integers

Author:
Yuguang Fang

Journal:
Proc. Amer. Math. Soc. **130** (2002), 1619-1622

MSC (2000):
Primary 11A63, 11A25, 11N37

Published electronically:
November 15, 2001

MathSciNet review:
1887007

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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper, a theorem on the asymptotic property of a summation of digits in a -adic representation is presented.

**1.**L. E. Bush,*An asymptotic formula for the average sum of the digits of integers*, Amer. Math. Monthly**47**(1940), 154–156. MR**0001225****2.**Richard Bellman and Harold N. Shapiro,*On a problem in additive number theory*, Ann. of Math. (2)**49**(1948), 333–340. MR**0023864****3.**L. Mirsky,*A theorem on representations of integers in the scale of 𝑟*, Scripta Math.**15**(1949), 11–12. MR**0030991****4.**Peh-Hsuin Cheo and Sze-Chien Yien,*A problem on the 𝑘-adic representation of positive integers*, Acta Math. Sinica**5**(1955), 433–438 (Chinese, with English summary). MR**0075979****5.**Hansraj Gupta,*Selected topics in number theory*, Abacus Press, Tunbridge Wells, 1980. MR**572086**

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Additional Information

**Yuguang Fang**

Affiliation:
Department of Electrical and Computer Engineering, University of Florida, 435 Engineering Building, P.O. Box 116130, Gainesville, Florida 32611-6130

Email:
fang@ece.ufl.edu

DOI:
https://doi.org/10.1090/S0002-9939-01-06303-1

Keywords:
$k$-adic,
asymptotic property,
arithmetic function,
number theory

Received by editor(s):
January 10, 2001

Published electronically:
November 15, 2001

Communicated by:
David E. Rohrlich

Article copyright:
© Copyright 2001
American Mathematical Society