Egyptian fractions: problems and progress

School of Mathematics Colloquium
Thursday, April 27, 2023 - 11:00am for 1 hour (actually 50 minutes)
Skiles 006
Thomas Bloom – University of Oxford –
Tom Kelly

The study of Egyptian fractions, representing rational numbers as the sum of distinct unit fractions, is one of the oldest areas of number theory. In this talk we will discuss some fascinating problems in the area, including both open problems and some recent progress, such as the solution to the Erdos-Graham conjecture: 1 can be written as the sum of unit fractions with denominators drawn from an arbitrary set of integers of positive density.