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{\bf Kellen Myers and Aaron Robertson}
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{\bf Two Color Off-diagonal Rado-type Numbers}
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We show that for any two linear homogeneous equations
${\cal E}_0,{\cal E}_1$, each with at least three variables and
coefficients not all the same sign, any 2-coloring of ${\Bbb Z}^+$
admits monochromatic solutions of color 0 to ${\cal E}_0$ or
monochromatic solutions of color 1 to ${\cal E}_1$. We define the
2-color off-diagonal Rado number $RR({\cal E}_0,{\cal E}_1)$ to
be the smallest $N$ such that $[1,N]$ must admit such solutions. We
determine a lower bound for $RR({\cal E}_0,{\cal E}_1)$ in
certain cases when each ${\cal E}_i$ is of the form
$a_1x_1+\dots+a_nx_n=z$ as well as find the exact value of
$RR({\cal E}_0,{\cal E}_1)$ when each is of the form
$x_1+a_2x_2+\dots+a_nx_n=z$. We then present a Maple package that
determines upper bounds for off-diagonal Rado numbers of a few
particular types, and use it to quickly prove two previous results for
diagonal Rado numbers.
\bye