CODEN(USA): JSERBR On some 2-color off-diagonal Rado numbers

Jing Jin
2017 Journal of Scientific and Engineering Research   unpublished
Let ε 0 , ε 1 be two equations, each with at least three variables and coefficients not all the same sign. Define the 2-color off-diagonal Rado number R 2 (ε 0 , ε 1) to be the smallest integer N such that for any 2-coloring of [1, N ], it must admit a monochromatic solution to ε 0 of the first color or a monochromatic solution to ε 1 of the second color. Motivated by Myers' open problem, we determine the exact numbers R 2 (2x+qy = z, 2x+ y = z) and R 2 (2x + 2qy = z, 2x + 2y = z) in this paper.