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Problems and results on combinatorial number theory III

  • Paul Erdös
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 626)

Keywords

Extremal Problem Small Integer Arithmetic Progression Infinite Sequence Combinatorial Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 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.MathSciNetzbMATHGoogle Scholar
  2. E. G. Straus, Nonaveraging sets, Proc. Symp. Pure Math. AMS 1967.Google Scholar
  3. 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.Google Scholar

References

  1. P. Erdös, On the integers of the form 2k+p and some related problems, Summa Brasil Math. 11(1950), 113–123.Google Scholar
  2. P. Erdös and E. Szemerédi, On a problem of Erdös and Stein, Acta Arithmetica 15(1968), 85–90.MathSciNetzbMATHGoogle Scholar
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  5. S. J. Benkoski and P. Erdös, On weird and pseudoperfect numbers, Math. Comp. 28(1974), 617–623.MathSciNetCrossRefzbMATHGoogle Scholar

References

  1. P. Erdös, On integers of the form 2k+p and some related problems, Summa Brasil Math. 2(1950), 113–123. For further literature on covering congruences see P. Erdös, Some problems in number theory, Computers in number theory, Proc. Atlas Symp. Oxford 1969 Acad. Press 1971, 405–414.MathSciNetGoogle Scholar
  2. A. Schinzel, Reducibility of polynomials, ibid., 73–75.Google Scholar
  3. 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.MathSciNetCrossRefzbMATHGoogle Scholar

References

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

References

  1. 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.MathSciNetzbMATHGoogle Scholar
  2. 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.MathSciNetCrossRefzbMATHGoogle Scholar
  3. 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).MathSciNetzbMATHGoogle Scholar
  4. 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.MathSciNetCrossRefzbMATHGoogle Scholar
  5. F. Krückeberg, B2-Folgen und verwandte Zahlenfolgen, J. reine angew Math. 206(1961), 53–60.MathSciNetzbMATHGoogle Scholar

References

  1. 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.MathSciNetCrossRefzbMATHGoogle Scholar

References

  1. I. Ruzsa, On a problem of P. Erdös, Canad. Math. Bull. 15(1972), 309–310.MathSciNetCrossRefGoogle Scholar
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  5. P. Erdös, Some applications of graph theory to number theory, Proc. second Chapel Hill conference on comb math., North Carolina, Chapel Hill, NC 1970, 136–145.Google Scholar
  6. P. Erdös, Some problems on consecutive prime numbers, Mathematika 19 (1972), 91–95.MathSciNetCrossRefzbMATHGoogle Scholar
  7. D. Hensley and Ian Richards, Primes in intervals, Acta Arithmetica 25 (1974), 375–391.MathSciNetzbMATHGoogle Scholar

References

  1. 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.MathSciNetGoogle Scholar
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References

  1. P. Erdös and W. H. J. Fuchs, On a problem of additive number theory, J. London Math. Soc. 31(1956), 67–73.MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag 1977

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  • Paul Erdös

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