{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 $k=3$.}
Shirdareh Haghighi, M. H., & Salehi Nowbandegani, P. (2012). On rainbow 4-term arithmetic progressions. Bulletin of the Iranian Mathematical Society, 37(No. 3), 33-37.
MLA
M. H. Shirdareh Haghighi; P. Salehi Nowbandegani. "On rainbow 4-term arithmetic progressions". Bulletin of the Iranian Mathematical Society, 37, No. 3, 2012, 33-37.
HARVARD
Shirdareh Haghighi, M. H., Salehi Nowbandegani, P. (2012). 'On rainbow 4-term arithmetic progressions', Bulletin of the Iranian Mathematical Society, 37(No. 3), pp. 33-37.
VANCOUVER
Shirdareh Haghighi, M. H., Salehi Nowbandegani, P. On rainbow 4-term arithmetic progressions. Bulletin of the Iranian Mathematical Society, 2012; 37(No. 3): 33-37.