Geodesic
On a coloring conjecture about unit fractions
Annals of mathematics, Tome 157 (2003) no. 2, pp. 545-556.

Voir la notice de l'article provenant de la source Annals of Mathematics website

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 $\sum_{n \in S} 1/n = 1$. 
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     author = {Ernest S. Croot, III},
     title = {On a coloring conjecture about unit fractions},
     journal = {Annals of mathematics},
     pages = {545--556},
     publisher = {mathdoc},
     volume = {157},
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     year = {2003},
     doi = {10.4007/annals.2003.157.545},
     mrnumber = {1973054},
     zbl = {1041.11019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4007/annals.2003.157.545/}
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Ernest S. Croot, III. On a coloring conjecture about unit fractions. Annals of mathematics, Tome 157 (2003) no. 2, pp. 545-556. doi : 10.4007/annals.2003.157.545. http://geodesic.mathdoc.fr/articles/10.4007/annals.2003.157.545/

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