Covering the integers by arithmetic sequences
Acta Arithmetica (1995)
- Volume: 72, Issue: 2, page 109-129
- ISSN: 0065-1036
Access Full Article
topHow to cite
topZhi Wei Sun. "Covering the integers by arithmetic sequences." Acta Arithmetica 72.2 (1995): 109-129. <http://eudml.org/doc/206788>.
@article{ZhiWeiSun1995,
author = {Zhi Wei Sun},
journal = {Acta Arithmetica},
keywords = {covering system; sums of reciprocal values of reals; arithmetic progressions; arithmetic sequences},
language = {eng},
number = {2},
pages = {109-129},
title = {Covering the integers by arithmetic sequences},
url = {http://eudml.org/doc/206788},
volume = {72},
year = {1995},
}
TY - JOUR
AU - Zhi Wei Sun
TI - Covering the integers by arithmetic sequences
JO - Acta Arithmetica
PY - 1995
VL - 72
IS - 2
SP - 109
EP - 129
LA - eng
KW - covering system; sums of reciprocal values of reals; arithmetic progressions; arithmetic sequences
UR - http://eudml.org/doc/206788
ER -
References
top- [1] M. A. Berger, A. Felzenbaum and A. S. Fraenkel, Improvements to the Newman-Znám result for disjoint covering systems, Acta Arith. 50 (1988), 1-13. Zbl0551.10003
- [2] R. B. Crittenden and C. L. Vanden Eynden, A proof of a conjecture of Erdős, Bull. Amer. Math. Soc. 75 (1969), 1326-1329. Zbl0186.07902
- [3] R. B. Crittenden and C. L. Vanden Eynden, Any n arithmetic progressions covering the first 2ⁿ integers cover all integers, Proc. Amer. Math. Soc. 24 (1970), 475-481. Zbl0192.39001
- [4] R. B. Crittenden and C. L. Vanden Eynden, The union of arithmetic progressions with differences not less than k, Amer. Math. Monthly 79 (1972), 630. Zbl0239.10031
- [5] P. Erdős, On integers of the form and some related problems, Summa Brasil. Math. 2 (1950), 113-123.
- [6] P. Erdős, Remarks on number theory IV: Extremal problems in number theory I, Mat. Lapok 13 (1962), 228-255.
- [7] P. Erdős, Problems and results on combinatorial number theory III, in: Number Theory Day, M. B. Nathanson (ed.), Lecture Notes in Math. 626, Springer, New York, 1977, 43-72.
- [8] P. Erdős, Problems and results in number theory, in: Recent Progress in Analytic Number Theory, H. Halberstam and C. Hooley (eds.), Vol. 1, Academic Press, London, 1981, 1-14.
- [9] R. K. Guy, Unsolved Problems in Number Theory, Springer, New York, 1981.
- [10] M. Newman, Roots of unity and covering sets, Math. Ann. 191 (1971), 279-282. Zbl0203.35205
- [11] Š. Porubský, Covering systems and generating functions, Acta Arith. 26 (1974/75), 223-231. Zbl0268.10044
- [12] Š. Porubský, On m times covering systems of congruences, Acta Arith. 29 (1976), 159-169. Zbl0282.10033
- [13] Š. Porubský, Results and problems on covering systems of residue classes, Mitt. Math. Sem. Giessen 1981, no. 150, 1-85. Zbl0479.10032
- [14] S. K. Stein, Unions of arithmetic sequences, Math. Ann. 134 (1958), 289-294. Zbl0084.04302
- [15] Z. W. Sun, Several results on systems of residue classes, Adv. in Math. (Beijing) 18 (1989), 251-252.
- [16] Z. W. Sun, An improvement to the Znám-Newman result, Chinese Quart. J. Math. 6 (3) (1991), 90-96.
- [17] Z. W. Sun, On exactly m times covers, Israel. J. Math. 77 (1992), 345-348. Zbl0768.11001
- [18] S. P. Tung, Complexity of sentences over number rings, SIAM J. Comp. 20 (1991), 126-143. Zbl0717.03002
- [19] M. Z. Zhang, A note on covering systems of residue classes, J. Sichuan Univ. (Nat. Sci. Ed.) 26 (1989), Special Issue, 185-188.
- [20] Š. Znám, On exactly covering systems of arithmetic sequences, Math. Ann. 180 (1969), 227-232. Zbl0169.37405
- [21] Š. Znám, A survey of covering systems of congruences, Acta Math. Univ. Comenian. 40/41 (1982), 59-79.
Citations in EuDML Documents
topNotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.