Some Problems and Results on Combinatorial Number Theory

I have written many papers with similar titles during my long life. I will try to write this paper in such a way that it will not entirely be contained in the union of the set of my previous papers and that a t least some of the open problems I state will not be entirely hopeless. Perhaps the most interesting and significant results are those connected with van der Waerden’s and SzemerCdi’s theorem, but since I and others have written a great deal about these questions, I will include only a short discussion of these problems at the end of the paper. For a rich source of solved and unsolved problems in combinatorial number theory, see [ 10,201. First of all I mention a few old problems and results. First a very simple old well-known result of mine.

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