Abstract   For integers  k ,  n ,  c  with  k ,   n  ≥  1   and   c  ≥  0  , the  n  color weak Rado number   W    R    k    (  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     x    1    +    x    2    +  …  +    x    k    +  c  =    x    k  +  1    , such that     x    i    ≠    x    j     when   i  ≠  j  . If no such  N  exists, then   W    R    k    (  n  ,  c  )   is defined as infinite.  In this work, we consider the main issue regarding the 3 color weak Rado number for the equation     x    1    +    x    2    +  c  =    x    3     and the exact value of the   W    R    2    (  3  ,  c  )  =  13  c  +  22   is established.
['M. P. Revuelta', 'Luis Boza', 'J.M. Marín', 'M.I. Sanz']
Exact value of 3 color weak Rado number