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Representation of m as

Published online by Cambridge University Press:  20 November 2018

R. C. Entringer
R. C. Entringer*
Affiliation:
University of New Mexico
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J.H. van Lint has recently shown [1] that if A(n, m) denotes the n number of representations of m in the form , where εk = 0 or 1 for -n ≤ k ≤ n then

(1)

Using this result, the fact that A(n, m) is a non-increasing function of |m|, and a simple recurrence relation for A(n, m) we derive the following extension of (1):

(2)

where [0 (n)] is any integral valued function m(n) = 0(n).

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 11 , Issue 2 , June 1968 , pp. 289 - 293
Copyright
Copyright © Canadian Mathematical Society 1968

References

1. van Lint, J. H., Representation of 0 as . Proc. Amer. Math. Soc. 18 (1967) 182-184.Google Scholar