This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
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.
E. G. Straus, Nonaveraging sets, Proc. Symp. Pure Math. AMS 1967.
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.
References
P. Erdös, On the integers of the form 2k+p and some related problems, Summa Brasil Math. 11(1950), 113–123.
P. Erdös and E. Szemerédi, On a problem of Erdös and Stein, Acta Arithmetica 15(1968), 85–90.
P. Erdös, On a problem on systems of congruences (in Hungarian) Mat. Lapok 3(1952), 122–128.
S. L. G. Choi, Covering the set of integers by congruence classes of distinct moduli, Math. Comp. 25(1971), 885–895.
S. J. Benkoski and P. Erdös, On weird and pseudoperfect numbers, Math. Comp. 28(1974), 617–623.
References
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.
A. Schinzel, Reducibility of polynomials, ibid., 73–75.
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.
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.
P. Erdös and A. Sárkozi, On the divisibility properties of sequences of integers, Proc. London Math. Soc., 21(1970), 97–101.
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.
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.
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).
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.
F. Krückeberg, B2-Folgen und verwandte Zahlenfolgen, J. reine angew Math. 206(1961), 53–60.
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.
References
I. Ruzsa, On a problem of P. Erdös, Canad. Math. Bull. 15(1972), 309–310.
P. Erdös and P. Turán, On some new questions on the distribution of prime numbers, Bull. Amer. Math. Soc. 59(1948), 271–278, see also P. Erdös, On the difference of consecutive primes, ibid 885–889.
P. Erdös and A. Rényi, Some problems and results on consecutive primes, Simon Stevin 27(1950), 115–126.
P. Erdös and K. Prachar, Sätze und Probleme über PK/K, Abh. Math. Sem. Univ. Hamburg 26(1962), 51–56.
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.
P. Erdös, Some problems on consecutive prime numbers, Mathematika 19 (1972), 91–95.
D. Hensley and Ian Richards, Primes in intervals, Acta Arithmetica 25 (1974), 375–391.
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.
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.
References
P. Erdös and W. H. J. Fuchs, On a problem of additive number theory, J. London Math. Soc. 31(1956), 67–73.
Editor information
Rights and permissions
Copyright information
© 1977 Springer-Verlag
About this paper
Cite this paper
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
Download citation
DOI: https://doi.org/10.1007/BFb0063064
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-08529-4
Online ISBN: 978-3-540-35985-2
eBook Packages: Springer Book Archive