2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/69323We 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 versionNumber Theory11P99text