Some solved and unsolved problems in combinatorial number theory, ii

P. Erdős; A. Sárközy

Colloquium Mathematicae (1993)

  • Volume: 65, Issue: 2, page 201-211
  • ISSN: 0010-1354

Abstract

top
In an earlier paper [9], the authors discussed some solved and unsolved problems in combinatorial number theory. First we will give an update of some of these problems. In the remaining part of this paper we will discuss some further problems of the two authors.

How to cite

top

Erdős, P., and Sárközy, A.. "Some solved and unsolved problems in combinatorial number theory, ii." Colloquium Mathematicae 65.2 (1993): 201-211. <http://eudml.org/doc/210214>.

@article{Erdős1993,
abstract = {In an earlier paper [9], the authors discussed some solved and unsolved problems in combinatorial number theory. First we will give an update of some of these problems. In the remaining part of this paper we will discuss some further problems of the two authors.},
author = {Erdős, P., Sárközy, A.},
journal = {Colloquium Mathematicae},
keywords = {additive number theory; multiplicative number theory; arithmetic functions; Sidon sets; representation problems of sequences of integers; number of distinct prime factors},
language = {eng},
number = {2},
pages = {201-211},
title = {Some solved and unsolved problems in combinatorial number theory, ii},
url = {http://eudml.org/doc/210214},
volume = {65},
year = {1993},
}

TY - JOUR
AU - Erdős, P.
AU - Sárközy, A.
TI - Some solved and unsolved problems in combinatorial number theory, ii
JO - Colloquium Mathematicae
PY - 1993
VL - 65
IS - 2
SP - 201
EP - 211
AB - In an earlier paper [9], the authors discussed some solved and unsolved problems in combinatorial number theory. First we will give an update of some of these problems. In the remaining part of this paper we will discuss some further problems of the two authors.
LA - eng
KW - additive number theory; multiplicative number theory; arithmetic functions; Sidon sets; representation problems of sequences of integers; number of distinct prime factors
UR - http://eudml.org/doc/210214
ER -

References

top
  1. [1] M. Ajtai, J. Komlós and E. Szemerédi, A dense infinite Sidon sequence, European J. Combin. 2 (1981), I-II. Zbl0474.10038
  2. [2] J. Beck, Roth's estimate of the discrepancy of integer sequences is nearly sharp, Combinatorica 1 (1981), 319-325. Zbl0491.10046
  3. [3] P. Erdős, Problems and results on consecutive integers, Publ. Math. Debrecen 23 (1976), 271-282. Zbl0353.10032
  4. [4] P. Erdős and R. Freud, On Sidon sequences and related problems, Mat. Lapok 1 (1991), 1-44 (in Hungarian with English summary). 
  5. [5] P. Erdős, C. Pomerance and A. Sárközy, On locally repeated values of certain arithmetic functions, I, J. Number Theory 21 (1985), 319-332. Zbl0574.10012
  6. [6] P. Erdős, C. Pomerance and A. Sárközy,On locally repeated values of certain arithmetic functions, II, Acta Math. Acad. Sci. Hungar. 49 (1987), 251-259. 
  7. [7] P. Erdős, C. Pomerance and A. Sárközy,On locally repeated values of certain arithmetic functions, III, Proc. Amer. Math. Soc. 101 (1987), 1-7. 
  8. [8] P. Erdős and A. Sárközy, On differences and sums of integers, II, Bull. Greek Math. Soc. 18 (1977), 204-223. 
  9. [9] P. Erdős and A. Sárközy, Some solved and unsolved problems in combinatorial number theory, Math. Slovaca 28 (1978), 407-421. Zbl0395.10002
  10. [10] P. Erdős and A. Sárközy, On products of integers, II, Acta Sci. Math. (Szeged) 40 (1978), 243-259. Zbl0401.10068
  11. [11] P. Erdős and A. Sárközy, On the prime factors of n k and of consecutive integers, Utilitas Math. 16 (1979), 197-215. Zbl0419.10040
  12. [12] P. Erdős and A. Sárközy, Some asymptotic formulas on generalized divisor functions, I, in: Studies in Pure Mathematics, To the Memory of Paul Turán, Akadémiai Kiadó, 1983, 165-179. 
  13. [13] P. Erdős and A. Sárközy, Some asymptotic formulas on generalized divisor functions, II, J. Number Theory 15 (1982), 115-136. Zbl0488.10043
  14. [14] P. Erdős and A. Sárközy, Some asymptotic formulas on generalized divisor functions, III, Acta Arith. 41 (1982), 395-411. Zbl0492.10037
  15. [15] P. Erdős and A. Sárközy, Some asymptotic formulas on generalized divisor functions, IV, Studia Sci. Math. Hungar. 15 (1980), 467-479. Zbl0512.10037
  16. [16] P. Erdős and A. Sárközy, Problems and results on additive properties of general sequences, I, Pacific J. Math. 118 (1985), 347-357. Zbl0569.10032
  17. [17] P. Erdős and A. Sárközy, Problems and results on additive properties of general sequences, II, Acta Math. Acad. Sci. Hungar. 48 (1986), 201-211. Zbl0621.10041
  18. [18] P. Erdős and A. Sárközy, On a conjecture of Roth and some related problems, II, in: Number Theory, Proc. First Conference of the Canadian Number Theory Association (Banff, Alberta, 1988), R. A. Mollin (ed.), Walter de Gruyter, Berlin 1990, 125-138. 
  19. [19] P. Erdős and A. Sárközy, On sets of coprime integers in intervals, Hardy-Ramanujan J., to appear. 
  20. [20] P. Erdős and A. Sárközy, Arithmetic progressions in subset sums, Discrete Math. 102 (1992), 249-264. Zbl0758.11007
  21. [21] P. Erdős, A. Sárközy and V. T. Sós, Problems and results on additive properties of general sequences, III, Studia Sci. Math. Hungar. 22 (1987), 53-63. Zbl0669.10078
  22. [22] P. Erdős, A. Sárközy and V. T. Sós, Problems and results on additive properties of general sequences, IV, in: Number Theory, Proceedings, Ootacamund, India 1984; Springer, 1985, 85-104. 
  23. [23] P. Erdős, A. Sárközy and V. T. Sós, Problems and results on additive properties of general sequences, V, Monatsh. Math. 102 (1986), 183-197. Zbl0597.10055
  24. [24] P. Erdős, A. Sárközy and V. T. Sós, On a conjecture of Roth and some related problems, I, in: Colloq. Math. Soc. János Bolyai, to appear. Zbl0689.10061
  25. [25] P. Erdős, A. Sárközy and V. T. Sós, On product representations of powers, I, to appear. Zbl0840.11010
  26. [26] P. Erdős, A. Sárközy and E. Szemerédi, On some extremal properties of sequences of integers, Ann. Univ. Sci. Budapest. Eötvös 12 (1969), 131-135. Zbl0188.34504
  27. [27] P. Erdős, A. Sárközy and E. Szemerédi, On some extremal properties of sequences of integers, II, Publ. Math. Debrecen 27 (1980), 117-125. Zbl0461.10047
  28. [28] P. Erdős and J. Selfridge, Some problems on the prime factors of consecutive integers, Illinois J. Math. 11 (1967), 428-430. Zbl0149.28901
  29. [29] J. Komlós, J. Pintz and E. Szemerédi, A lower bound for Heilbronn's problem, J. London Math. Soc. (2) 25 (1982), 13-24. Zbl0483.52008
  30. [30] K. F. Roth, On a problem of Heilbronn, ibid. (1) 26 (1951), 198-204. Zbl0043.16303
  31. [31] K. F. Roth, Remark concerning integer sequences, Acta Arith. 9 (1964), 257-260. Zbl0125.29601
  32. [32] I. Z. Ruzsa, On measures of intersectivity, Acta Math. Hungar. 43 (1984), 335-340. Zbl0534.10047
  33. [33] R. P. Stanley, Weyl groups, the hard Lefschetz theorem and the Sperner property, SIAM J. Algebraic Discrete Methods 1 (1980), 168-184. Zbl0502.05004
  34. [34] A. Stöhr, Gelöste und ungelöste Fragen über Basen der natürlichen Zahlenreihe, II, J. Reine Angew. Math. 194 (1955), 111-140. 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.