# Some solved and unsolved problems in combinatorial number theory, ii

Colloquium Mathematicae (1993)

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

## Access Full Article

top## Abstract

top## How to cite

topErdős, 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] M. Ajtai, J. Komlós and E. Szemerédi, A dense infinite Sidon sequence, European J. Combin. 2 (1981), I-II. Zbl0474.10038
- [2] J. Beck, Roth's estimate of the discrepancy of integer sequences is nearly sharp, Combinatorica 1 (1981), 319-325. Zbl0491.10046
- [3] P. Erdős, Problems and results on consecutive integers, Publ. Math. Debrecen 23 (1976), 271-282. Zbl0353.10032
- [4] P. Erdős and R. Freud, On Sidon sequences and related problems, Mat. Lapok 1 (1991), 1-44 (in Hungarian with English summary).
- [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] 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] 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] P. Erdős and A. Sárközy, On differences and sums of integers, II, Bull. Greek Math. Soc. 18 (1977), 204-223.
- [9] P. Erdős and A. Sárközy, Some solved and unsolved problems in combinatorial number theory, Math. Slovaca 28 (1978), 407-421. Zbl0395.10002
- [10] P. Erdős and A. Sárközy, On products of integers, II, Acta Sci. Math. (Szeged) 40 (1978), 243-259. Zbl0401.10068
- [11] P. Erdős and A. Sárközy, On the prime factors of $\left(\genfrac{}{}{0pt}{}{n}{k}\right)$ and of consecutive integers, Utilitas Math. 16 (1979), 197-215. Zbl0419.10040
- [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] P. Erdős and A. Sárközy, Some asymptotic formulas on generalized divisor functions, II, J. Number Theory 15 (1982), 115-136. Zbl0488.10043
- [14] P. Erdős and A. Sárközy, Some asymptotic formulas on generalized divisor functions, III, Acta Arith. 41 (1982), 395-411. Zbl0492.10037
- [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] 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] 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] 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] P. Erdős and A. Sárközy, On sets of coprime integers in intervals, Hardy-Ramanujan J., to appear.
- [20] P. Erdős and A. Sárközy, Arithmetic progressions in subset sums, Discrete Math. 102 (1992), 249-264. Zbl0758.11007
- [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] 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] 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] 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] P. Erdős, A. Sárközy and V. T. Sós, On product representations of powers, I, to appear. Zbl0840.11010
- [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] 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] P. Erdős and J. Selfridge, Some problems on the prime factors of consecutive integers, Illinois J. Math. 11 (1967), 428-430. Zbl0149.28901
- [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] K. F. Roth, On a problem of Heilbronn, ibid. (1) 26 (1951), 198-204. Zbl0043.16303
- [31] K. F. Roth, Remark concerning integer sequences, Acta Arith. 9 (1964), 257-260. Zbl0125.29601
- [32] I. Z. Ruzsa, On measures of intersectivity, Acta Math. Hungar. 43 (1984), 335-340. Zbl0534.10047
- [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] A. Stöhr, Gelöste und ungelöste Fragen über Basen der natürlichen Zahlenreihe, II, J. Reine Angew. Math. 194 (1955), 111-140.

## NotesEmbed ?

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