## A generalization of Schur Numbers

Consider the integer linear equation $\sum_{i=1}^{n} c_ix_i=0$ where $c_i(\ne 0) \in Z$. Supposing it is given that there is a natural number N such that, if {1,2...N} is partitioned in two sets, one of these always contains a solution of the equation. The minimal such N is called the Rado number of the equation. I am looking for general bounds on such N, in the cases where it exists. Where can I possibly find such results. Thanks.

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 Are you looking for information in terms of the $c_i$? – drvitek Sep 18 2010 at 5:55