Geodesic
On rainbow arithmetic progressions
The electronic journal of combinatorics, Tome 11 (2004) no. 1
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Consider natural numbers $\{1, \cdots, n\}$ colored in three colors. We prove that if each color appears on at least $(n+4)/6$ numbers then there is a three-term arithmetic progression whose elements are colored in distinct colors. This variation on the theme of Van der Waerden's theorem proves the conjecture of Jungić et al.
DOI : 10.37236/1754
Classification : 11B25, 11B75, 05D10
Mots-clés : coloring of integers 
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     author = {Maria Axenovich and Dmitri Fon-Der-Flaass},
     title = {On rainbow arithmetic progressions},
     journal = {The electronic journal of combinatorics},
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     number = {1},
     doi = {10.37236/1754},
     zbl = {1060.11005},
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Maria Axenovich; Dmitri Fon-Der-Flaass. On rainbow arithmetic progressions. The electronic journal of combinatorics, Tome 11 (2004) no. 1. doi: 10.37236/1754

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