# On a coloring conjecture about unit fractions

### Abstract

We prove an old conjecture of Erdős and Graham on sums of unit fractions: There exists a constant $b>0$ such that if we $r$-color the integers in $[2,b^r]$, then there exists a monochromatic set $S$ such that $\sum_{n \in S} 1/n = 1$.

## Authors

Ernest S. Croot, III