most recent 30 from http://mathoverflow.net 2013-05-25T20:32:55Z http://mathoverflow.net/feeds/user/9330 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/39198/a-generalization-of-schur-numbers Shahab 2010-09-18T04:17:34Z 2010-09-18T04:17:34Z

<p>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.</p>