Determination of the two-color Rado number for $a_1{x}_1+...+a_m{x}_m=x_0$

Song Guo, Zhi-Wei Sun

For positive integers $a_1,a_2,...,a_m$, we determine the least positive integer $R(a_1,...,a_m)$ such that for every 2-coloring of the set $[1,n]=1,...,n$ with $n\ge R(a_1,...,a…