On a coloring conjecture about unit fractions

Abstract

We prove an old conjecture of Erd{\H o}s 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 ${\sum }_{n\in S}1/n=1$.

12 pages published version