On the number of sums of three unit fractions

Simon Brown
Notes on Number Theory and Discrete Mathematics, ISSN 1310–5132
Volume 19, 2013, Number 4, Pages 23–32
Full paper (PDF, 92 Kb)


Authors and affiliations

Simon Brown
School of Human Life Sciences, University of Tasmania
Locked Bag 1320, Launceston, Tasmania 7250, Australia


Rational fractions can often be expressed as the sum of three unit fractions and, generally, such a fraction can be expanded in several ways. An estimate of the maximum number of possible solutions is given. An expression for five possible solutions is given and this is used to obtain several general expansions.


  • Polynomials
  • Unit fractions

AMS Classification

  • 11D68


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Cite this paper

Brown, S. (2013). On the number of sums of three unit fractions. Notes on Number Theory and Discrete Mathematics, 19(4), 28-32.

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