Exact value of 3 color weak Rado number

For integers k, n, c with k, n≥1 and c≥0, the n color weak Rado number WRk(n,c) is defined as the least integer N, if it exists, such that for every n-coloring of the set {1,2,…,N}, there exists a monochromatic solution in that set to the equation x1+x2+…+xk+c=xk+1, such that xi≠xj when i≠j. If no such N exists, then WRk(n,c) is defined as infinite.In this work, we consider the main issue regarding the 3 color weak Rado number for the equation x1+x2+c=x3 and the exact value of the WR2(3,c)=13c+22 is established.