Dense Egyptian Fractions
| dc.creator | Martin, Greg | |
| dc.date | 1998-04-08 | |
| dc.date.accessioned | 2026-07-07T05:24:21Z | |
| dc.date.available | 2026-07-07T05:24:21Z | |
| dc.description | Every positive rational number has representations as Egyptian fractions (sums of reciprocals of distinct positive integers) with arbitrarily many terms and with arbitrarily large denominators. However, such representations normally use a very sparse subset of the positive integers up to the largest demoninator. We show that for every positive rational there exist Egyptian fractions whose largest denominator is at most N and whose denominators form a positive proportion of the integers up to N, for sufficiently large N; furthermore, the proportion is within a small factor of best possible. | |
| dc.description | 16 pages; to appear in Trans. Amer. Math. Soc | |
| dc.identifier | https://arxiv.org/abs/math/9804045 | |
| dc.identifier | http://arxiv.org/abs/math/9804045 | |
| dc.identifier | Trans. Amer. Math. Soc. 351 (1999), no. 9, pp. 3641-3657. | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/76807 | |
| dc.subject | Number Theory | |
| dc.subject | 11D68 | |
| dc.title | Dense Egyptian Fractions | |
| dc.type | text |