Denser Egyptian fractions

  title={Denser Egyptian fractions},
  author={G. Martin},
  journal={Acta Arithmetica},
  • 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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