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On some questions of Erdős and Graham about Egyptian fractions

Part of: Diophantine equations

Published online by Cambridge University Press:  26 February 2010

Ernest S. Croot III
Ernest S. Croot III
Affiliation:
Department of Mathematics, The University of Georgia, Athens, GA 30602, U.S.A.
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Abstract

In this paper it is proved that, for x sufficiently large, every integer m with

can be written as m = Σ1≤n≤xεn/n, where εi, = 0 or 1.

MSC classification

Secondary: 11D68: Rational numbers as sums of fractions
Type
Research Article
Information
Mathematika , Volume 46 , Issue 2 , December 1999 , pp. 359 - 372
Copyright
Copyright © University College London 1999

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References

1. Erdős, Pál and Graham, R. L.. Old and new problems and results in combinatorial number theory. L'Enseignement Mathématique Université de Genève, 103 (1980), 39 40.Google Scholar
2. Guy, Richard K.. Unsolved Problems in Number Theory, second edition (Springer, 1994). 158 166.CrossRefGoogle Scholar
3. Nagell, Trygve. Introduction to Number Theory, Second Edition (Chelsea, 1964), 54–67.Google Scholar
4. Rosser, J. B. and Shoenfeld, Lowell, Approximate formulas for some functions of prime numbers, Illinois J. Math., 6 (1962), 70.CrossRefGoogle Scholar
5. Yokota, Hisashi. On number of integers representable as a sum of unit fractions. II. J. Number Theory, 67 (1997), 162–169. (Corrigendum. J. Number Theory, 72 (1998), 150.)CrossRefGoogle Scholar