Shi-Sheng Li

Unit fractions with semiprime denominators: an elementary proof of Erd\H{o}s Problem #306

We give an elementary proof that every positive rational number $a/b$ with $b$ squarefree is a finite sum of distinct unit fractions $1/n$, where each $n$ is a product of two distinct primes (Erd\H{o}s Problem #306). After a reduction to small targets, we take a single complete bipartite graph between the primes in $(y...