On a coloring conjecture about unit fractions


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 $\sum_{n \in S} 1/n = 1$.


Ernest S. Croot, III

Current address:

School of Mathematcs, Georgia Institute of Technology, 103 Skiles, Atlanta, GA 30332