HackerPapers

arXiv:math/0311421math.NT

On a coloring conjecture about unit fractions

Ernest S. Croot

Early discovery. Linked by one identifiable commenter. This paper is outside the main ranking; a mention is not an endorsement.

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

arXiv comments
12 pages published version
Journal reference
Ann. of Math. (2), Vol. 157 (2003), no. 2, 545--556
DOI
Subjects
math.NTNumber Theory

On Hacker News

Linked by 1 identifiable commenter in 1 comment across 1 thread, from Jan 2016 to Jan 2016.

Comments linking this paper, per year.

Discussed in comments1 thread

  1. New Erdős Paper Solves Egyptian Fraction Problem 1 comment

    • If you want to explore Egyptian Fractions more, here is a paper focusing on the Erdős-Graham problem [1.]: "On a Coloring Conjecture about Unit Fractions" by Ernest Croot [2.] [1.] https://en.wikipedia.org/wiki/Erd%C5%91s%E2%80%93Graham_prob... [2.]…

      dpflanView on HNParent context

Submitted to Hacker News

Connected through shared HN threads, not inferred similarity or a recommendation.