Simon Brown

Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132

Volume 20, 2014, Number 2, Pages 61—64

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## Details

### Authors and affiliations

Simon Brown

*The Deviot Institute, Deviot, Tasmania 7275, Australia and
School of Human Life Sciences, University of Tasmania,
Locked Bag 1320, Launceston, Tasmania 7250, Australia*

### Abstract

Of those fractions (*a / b* < 1) that can not be expressed as a sum of three unit fractions, many can be written in terms of three unit fractions if the smallest denominator is ⎣*b / a* ⎦ and the next largest denominator is < 0. General expressions are given for some specific classes of these. Two examples of Yamamoto are reconsidered.

### Keywords

- Unit fraction

### AMS Classification

- 11D68

### References

- Brown, S. Bounds of the denominators of Egyptian fractions, World Applied Programming, Vol. 2, 2012, 425‒430.
- Brown, S. On the number of sums of three unit fractions, Notes on Number Theory and Discrete Mathematics, Vol. 19, 2013, No. 4, 28‒32.
- Sierpinski, W. Sur les décompositions de nombres rationnels en fractions primaires, Mathesis, Vol. 65, 1956, 16‒32.
- Vaughan, R. C. On a problem of Erdös, Straus and Schinzel, Matematika, Vol. 17,

1970, 193‒198. - Vose, M. D. Egyptian fractions, Bulletin of the London Mathematical Society, Vol. 17, 1985, 21‒24.
- Webb, W. A. Rationals not expressible as a sum of three unit fractions, Elemente der Mathematik, Vol. 29, 1974, 1‒6.
- Yamamoto, K. On a conjecture of Erdös, Memoirs of the Faculty of Science, Kyushu University, Vol. 18, 1964, 166‒167.

## Related papers

- Brown, S. On the number of sums of three unit fractions, Notes on Number Theory and Discrete Mathematics, Vol. 19, 2013, No. 4, 28‒32.

## Cite this paper

APABrown, S. (2014). On rational fractions not expressible as a sum of three unit fractions. Notes on Number Theory and Discrete Mathematics, 20(2), 61-64.

ChicagoBrown, Simon. “On Rational Fractions Not Expressible as a Sum of Three Unit Fractions.” Notes on Number Theory and Discrete Mathematics 20, no. 2 (2014): 61-64.

MLABrown, Simon. “On Rational Fractions Not Expressible as a Sum of Three Unit Fractions.” Notes on Number Theory and Discrete Mathematics 20.2 (2014): 61-64. Print.