A Survey of Problems in Combinatorial Number Theory
نویسنده
چکیده
During my long life I published and stated many conjectures and wrote several papers which consisted entirely of stating old and new problems . In this paper I hope to survey some of them not to make the paper too long I restrict myself to problems on the borderline of combinatorics and number theory fields which are as stated in a previous paper closest to my heart or rather than to my brain. Again, to avoid excessive length, I restrict myself as much as possible to problems which either were raised by my collaborators and myself, or we worked on them. I do not want to imply that these problems are more interesting or important than the ones I neglect, but I am likely to know more about my own problems than the reader and finally, despite my great age, my memory and mind are still more or less intact . Thus I remember how and why I or we came to consider these problems, and what are the connections with other questions . First, I list some of my papers in which relevant problems are stated . (i) Problems and results on combinatorial number theory I, II, II' and III. Paper I was given at the first conference at Fort Collins (in honor of Professor Bose) also edited by Srivastava: A survey of combinatorial theory (North Holland Amsterdam, 1973) 117-138; the pair II and II' is due to my mistake : II' should have been III, II is in Journée Arithmetique de Bordeaux, Astérisque 24-25 (Juin 1974), 295-210, and II' is in J . Indian Math . Soc. 40 (1976) 285-298. Paper III is in Number theory day, held at Rockerfeller Univ ., edited by M . Natanson, Lecture Notes in Mathematics 626 (Springer Verlag, Berlin) 43-72 . (ii) Some older papers of mine : Quelques problémes de la théorie des nombres, Monographies de 1'Enseignement Mathématique No . 6, Univ. de Geneva (1963) 81-135 . Graham and I will soon publish a long paper in the same journal which brings this paper up to date and give also many new problems . P. Erdős, Some unsolved problems, Michigan Math. J. 4 (1957) 291-300 and Publ. Math . Inst . Hung. Acad. Sci . 6 (1961) 2216-254. The paper in Michigan Math. Journal was my first paper on unsolved problems . P. Erdős, Extremal problems in number theory, Proc . Symp . in Pure Math . VIII, Theory of Numbers (Amer . Math. Soc., Providence, RI, 1965) 181-189 . Several of the results stated in this paper were improved and extended in various papers by S.L.R. Choi . P. Erdős, Some recent advances and current problems in number theory,
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