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.
@article{bwmeta1.element.bwnjournal-article-cmv65i2p201bwm,
author = {P. Erd\H os and A. S\'ark\"ozy},
title = {Some solved and unsolved problems in combinatorial number theory, ii},
journal = {Colloquium Mathematicae},
volume = {66},
year = {1993},
pages = {201-211},
zbl = {0909.11010},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-cmv65i2p201bwm}
}
Erdős, P.; Sárközy, A. Some solved and unsolved problems in combinatorial number theory, ii. Colloquium Mathematicae, Tome 66 (1993) pp. 201-211. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv65i2p201bwm/
[000] [1] M. Ajtai, J. Komlós and E. Szemerédi, A dense infinite Sidon sequence, European J. Combin. 2 (1981), I-II. | Zbl 0474.10038
[001] [2] J. Beck, Roth's estimate of the discrepancy of integer sequences is nearly sharp, Combinatorica 1 (1981), 319-325. | Zbl 0491.10046
[002] [3] P. Erdős, Problems and results on consecutive integers, Publ. Math. Debrecen 23 (1976), 271-282. | Zbl 0353.10032
[003] [4] P. Erdős and R. Freud, On Sidon sequences and related problems, Mat. Lapok 1 (1991), 1-44 (in Hungarian with English summary).
[004] [5] P. Erdős, C. Pomerance and A. Sárközy, On locally repeated values of certain arithmetic functions, I, J. Number Theory 21 (1985), 319-332. | Zbl 0574.10012
[005] [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.
[006] [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.
[007] [8] P. Erdős and A. Sárközy, On differences and sums of integers, II, Bull. Greek Math. Soc. 18 (1977), 204-223.
[008] [9] P. Erdős and A. Sárközy, Some solved and unsolved problems in combinatorial number theory, Math. Slovaca 28 (1978), 407-421. | Zbl 0395.10002
[009] [10] P. Erdős and A. Sárközy, On products of integers, II, Acta Sci. Math. (Szeged) 40 (1978), 243-259. | Zbl 0401.10068
[010] [11] P. Erdős and A. Sárközy, On the prime factors of and of consecutive integers, Utilitas Math. 16 (1979), 197-215. | Zbl 0419.10040
[011] [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.
[012] [13] P. Erdős and A. Sárközy, Some asymptotic formulas on generalized divisor functions, II, J. Number Theory 15 (1982), 115-136. | Zbl 0488.10043
[013] [14] P. Erdős and A. Sárközy, Some asymptotic formulas on generalized divisor functions, III, Acta Arith. 41 (1982), 395-411. | Zbl 0492.10037
[014] [15] P. Erdős and A. Sárközy, Some asymptotic formulas on generalized divisor functions, IV, Studia Sci. Math. Hungar. 15 (1980), 467-479. | Zbl 0512.10037
[015] [16] P. Erdős and A. Sárközy, Problems and results on additive properties of general sequences, I, Pacific J. Math. 118 (1985), 347-357. | Zbl 0569.10032
[016] [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. | Zbl 0621.10041
[017] [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.
[018] [19] P. Erdős and A. Sárközy, On sets of coprime integers in intervals, Hardy-Ramanujan J., to appear.
[019] [20] P. Erdős and A. Sárközy, Arithmetic progressions in subset sums, Discrete Math. 102 (1992), 249-264. | Zbl 0758.11007
[020] [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. | Zbl 0669.10078
[021] [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.
[022] [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. | Zbl 0597.10055
[023] [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. | Zbl 0689.10061
[024] [25] P. Erdős, A. Sárközy and V. T. Sós, On product representations of powers, I, to appear. | Zbl 0840.11010
[025] [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. | Zbl 0188.34504
[026] [27] P. Erdős, A. Sárközy and E. Szemerédi, On some extremal properties of sequences of integers, II, Publ. Math. Debrecen 27 (1980), 117-125. | Zbl 0461.10047
[027] [28] P. Erdős and J. Selfridge, Some problems on the prime factors of consecutive integers, Illinois J. Math. 11 (1967), 428-430. | Zbl 0149.28901
[028] [29] J. Komlós, J. Pintz and E. Szemerédi, A lower bound for Heilbronn's problem, J. London Math. Soc. (2) 25 (1982), 13-24. | Zbl 0483.52008
[029] [30] K. F. Roth, On a problem of Heilbronn, ibid. (1) 26 (1951), 198-204. | Zbl 0043.16303
[030] [31] K. F. Roth, Remark concerning integer sequences, Acta Arith. 9 (1964), 257-260. | Zbl 0125.29601
[031] [32] I. Z. Ruzsa, On measures of intersectivity, Acta Math. Hungar. 43 (1984), 335-340. | Zbl 0534.10047
[032] [33] R. P. Stanley, Weyl groups, the hard Lefschetz theorem and the Sperner property, SIAM J. Algebraic Discrete Methods 1 (1980), 168-184. | Zbl 0502.05004
[033] [34] A. Stöhr, Gelöste und ungelöste Fragen über Basen der natürlichen Zahlenreihe, II, J. Reine Angew. Math. 194 (1955), 111-140.