New Results in Egyptian Fractions
by
Ernie Croot
The University of Georgia

This talk will be a survey of results in the theory of Egyptian Fractions, including recent results by myself and by Greg Martin. One such result is that given any rational r > 0, and for any N > 1, there exist integers n₁, ..., n_k, k variable, such that

N <= n1 < n2 < ... < nk <= ( er + Or (loglogN / logN)) N,

and

r =  1 n1 +  1 n2 + ... +  1 nk .

Moreover, the error term O_r(loglogN/logN) is best-possible. This result answers several questions posed by Erdos, R. Graham, and others.

Date received: April 14, 1999

Copyright © 1999 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cacu-09.