@article {
author = {Shirdareh Haghighi, M. H. and Salehi Nowbandegani, P.},
title = {On rainbow 4-term arithmetic progressions},
journal = {Bulletin of the Iranian Mathematical Society},
volume = {37},
number = {No. 3},
pages = {33-37},
year = {2012},
publisher = {Iranian Mathematical Society (IMS)},
issn = {1017-060X},
eissn = {1735-8515},
doi = {},
abstract = {{sl Let $[n]={1,dots, n}$ be colored in $k$ colors. A rainbow AP$(k)$ in $[n]$ is a $k$ term arithmetic progression whose elements have different colors. Conlon, Jungi'{c} and Radoiv{c}i'{c} cite{conlon} prove that there exists an equinumerous 4-coloring of $[4n]$ which is rainbow AP(4) free, when $n$ is even. Based on their construction, we show that such a coloring of $[4n]$ also exists for odd $n>1$. We conclude that for nonnegative integers $kgeq 3$ and $n > 1$, every equinumerous $k$-coloring of $[kn]$ contains a rainbow AP$(k)$ if and only if $k=3$.}},
keywords = {Rainbow arithmetic progression,4-term arithmetic progression,AP(4),AP($k$)},
url = {http://bims.iranjournals.ir/article_350.html},
eprint = {http://bims.iranjournals.ir/article_350_89e63dba5b5df3fefe16dd3a01425b8e.pdf}
}