Denser Egyptian fractions

@article{Martin1998DenserEF,
  title={Denser Egyptian fractions},
  author={G. Martin},
  journal={Acta Arithmetica},
  year={1998},
  volume={95},
  pages={231-260}
}
  • G. Martin
  • Published 1998
  • Mathematics
  • Acta Arithmetica
  • An Egyptian fraction is a sum of distinct unit fractions (reciprocals of positive integers). We show that every rational number has Egyptian fraction representations where the number of terms is of the same order of magnitude as the largest denominator, improving a result from an earlier paper to best-possible form. We also settle, in best-possible form, the related problem of how small M_t(r) can be such that there is an Egyptian fraction representation of r with exactly t terms, the… CONTINUE READING
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    References

    Publications referenced by this paper.
    SHOWING 1-10 OF 15 REFERENCES
    Dense Egyptian fractions
    • 17
    • Open Access
    On the number of positive integers ≦ x and free of prime factors > y
    • 179
    • Open Access
    A new algorithm for the expansion of Egyptian fractions
    • 15
    • Open Access
    Integers without large prime factors
    • 243
    • Open Access
    On unit fractions with denominators in short intervals
    • 7
    • Open Access
    On a problem of Erdős and Graham
    • 2
    • Open Access