Title: Egyptian fractions, practical numbers and the distribution of divisors
Abstract: The problem of expressing a rational number as a sum of distinct unit fraction goes back to the ancient Egyptians. In his study of Egyptian fractions, Fibonacci used the so-called practical numbers, which are those positive integers n such that all smaller positive integers can be expressed as sums of distinct divisors of n. We will discuss the history and recent advances in our understanding of Egyptian fractions, practical numbers and the distribution of divisors of integers.