On Monochromatic Solutions of Linear Equations Using At Least Three Colors

We study the number of monochromatic solution to linear equation in $\{1,\dots ,n\}$ when we color the set by at least three colors. We consider the $r$-commonness for $r\ge 3$ of linear equation with odd number of terms, and we also prove that any $2$-uncommon equation is $r$-uncommon for any $r\ge 3$.