Given a poistive integer $ m, $ determine the smallest integer $ n\ge 2 $ such that for any coloring of the $ n^2 $ unit squares of a $ n\times n $ square with $ m $ colors, there are, at least, two unit squares $ (i,j),(k,l) $ that share the same color, where $ 1\le i,j,k,l\le n,i\neq j,k\neq l. $ American Mathematical Monthly