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Sums of Fractions with Bounded Numerators

Published online by Cambridge University Press:  20 November 2018

B. M. Stewart  and
W. A. Webb
B. M. Stewart
Affiliation:
Michigan State University
W. A. Webb
Affiliation:
Michigan State University
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The general problem considered in this paper is that of sums of a finite number of reduced fractions whose numerators are elements of a finite set S of integers, and whose denominators are distinct positive integers. Egyptian, or unit, fractions are merely the case S = ﹛1﹜. Problems concerning these fractions have been treated extensively. Another specific case S = ﹛1, — 1﹜ has been treated by Sierpinski (2).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 18 , 1966 , pp. 999 - 1003
Copyright
Copyright © Canadian Mathematical Society 1966

References

1. Graham, R. L., On finite sums of unit fractions, Proc. London Math. Soc., 14 (1964), 193–207.Google Scholar
2. Sierpinski, W., Sur les décompositions de nombres rationnels en fractions primaires, Mathesis, 65 (1956), 16–32.Google Scholar
3. Smith, H. J. S., On the integration of discontinuous functions (1875), Collected Mathematical Papers, Vol. II (New York, 1965), 91–93.Google Scholar
4. Stewart, B. M., Theory of numbers, 2nd ed. (New York, 1964), 198–207.Google Scholar
5. van Albada, P. J. and van Lint, J. H., Reciprocal bases for the integers, Amer. Math. Monthly, 70 (1963), 170–174.Google Scholar