On a coloring conjecture about unit fractions

Details On a coloring conjecture about unit fractions On a coloring conjecture about unit fractions

2003-11-24

arxiv.org/abs/math/0311421v1

Ann. of Math. (2), Vol. 157 (2003), no. 2, 545--556

Mathematics

Number Theory

12 pages published version

Scientific paper

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

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