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A theorem on the -adic representation of positive integers

Author(s): Yuguang Fang
Journal: Proc. Amer. Math. Soc. 130 (2002), 1619-1622.
MSC (2000): Primary 11A63, 11A25, 11N37
Posted: November 15, 2001
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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.

References:

1.: L. E. Bush, An asymptotic formula for the average sum of the digits of integers, Amer. Math. Monthly 47 (1940), 154-156. MR 1:199f
2.: R. Bellman and H. N. Shapiro, On a problem in additive number theory, Ann. of Math. (2) 49 (1948), 333-340. MR 9:414a
3.: L. Mirsky, A theorem on representation of integers in the scale of , Scripta Math. 15 (1949), 11-12. MR 11:83g
4.: P. H. Cheo and Y. C. Yien, A problem on the -adic representation of positive integers, Acta Math. Sinica 5 (1955), 433-438. MR 17:828b
5.: H. Gupta, Selected Topics in Number Theory, ABACUS Press, 1980. MR 81e:10002

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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: 10.1090/S0002-9939-01-06303-1
PII: S 0002-9939(01)06303-1
Keywords: $k$-adic, asymptotic property, arithmetic function, number theory
Received by editor(s): January 10, 2001
Posted: November 15, 2001
Communicated by: David E. Rohrlich
Copyright of article: Copyright 2001, American Mathematical Society


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