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Problems and results on combinatorial number theory III

Part of the Lecture Notes in Mathematics book series (LNM,volume 626)

Keywords

  • Extremal Problem
  • Small Integer
  • Arithmetic Progression
  • Infinite Sequence
  • Combinatorial Theory

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References

  • E. Szemerédi, On sets of integers containing no k elements in arithmetic progression, Acta Arith. 27(1975), 299–345. For further literature and history of the problem see I; II and the paper of Szemeredi.

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  • E. G. Straus, Nonaveraging sets, Proc. Symp. Pure Math. AMS 1967.

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  • P. Erdös and E. G. Straus, Nonaveraging sets II, Coll. Math. Bólyai Math. Soc. Combinatorial theory and its applications, North Holland Amsterdam-London 1970 Vol. 2, 405–411.

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References

References

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  • A. Schinzel, Reducibility of polynomials, ibid., 73–75.

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  • F. Cohen and J. L. Selfridge, Not every number is the sum or difference of two prime powers, Math. of Computation 29(1975), 79–82.

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References

  • P. Erdös, Problems and results in additive number theory, Colloque sur la théorie des nombres, Bruxelles. George Thone, Liège; Masson and Cie, Paris (1955), 127–137.

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  • P. Erdös and A. Sárkozi, On the divisibility properties of sequences of integers, Proc. London Math. Soc., 21(1970), 97–101.

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References

  • P. Erdös and A. Rényi, Additive properties of random sequences of positive integers, Acta Arith 6(1960), 83–110, see also Halberstam-Roth, Sequences, Oxford Univ. Press, 1966.

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  • P. Erdös and P. Turán, On a problem of Sidon in additive number theory and on some related problems, Journal London Math. Soc. 16(1941), 212–216, Addendum 19(1944), 208.

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  • A. Stöhr, Gelöste und ungelöste Fragen über Basen der natürlichen Zahlenreihe I, II J. reine angew Math. 194(1955), 40–65, 111–140. This paper has many problems and results and a very extensive bibliography. It contains the proof of (1) and (5).

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  • C. Treash, The completion of finite incomplete Steiner triple systems with applications to loop theory, J. Combinatorial Theory, Ser A 10(1971), 259–265, for a sharper result C. C. Lindner, Embedding partial Steiner triple systems, ibid 18(1975), 349–351.

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References

  • Neil Hindman, Finite sums with sequences within cells of a partition of n, J. Combinatorial Theory Ser A 17(1974), 1–11, J. Baumgartner, ibid. 384–386.

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  • I. Ruzsa, On a problem of P. Erdös, Canad. Math. Bull. 15(1972), 309–310.

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References

  • P. Erdös, On some applications of graph theory to number theoretic problems, Publ. Ramanujan Inst. 1(1969), 131–136, see also Some applications of graph theory to number theory, The many facets of graph theory Proc. Conf. Western Michigan Univ. Kalamazoo 1968 Springer Verlag, Berlin 1969, 77–82.

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  • P. Erdös, A. Sárközi and E. Szemerédi, On divisibility properties of sequences of integers Number theory Colloquium Bólyai Math. Soc. North Holland 2(1968), 36–49.

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References

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© 1977 Springer-Verlag

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Erdös, P. (1977). Problems and results on combinatorial number theory III. In: Nathanson, M.B. (eds) Number Theory Day. Lecture Notes in Mathematics, vol 626. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0063064

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  • DOI: https://doi.org/10.1007/BFb0063064

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