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1995 | 72 | 2 | 109-129
Tytuł artykułu

Covering the integers by arithmetic sequences

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
Słowa kluczowe
Czasopismo
Rocznik
Tom
72
Numer
2
Strony
109-129
Opis fizyczny
Daty
wydano
1995
otrzymano
1993-11-18
poprawiono
1994-08-23
Twórcy
autor
  • Department of Mathematics, Nanjing University, Nanjing 210093, People's Republic of China
Bibliografia
  • [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.
  • [2] R. B. Crittenden and C. L. Vanden Eynden, A proof of a conjecture of Erdős, Bull. Amer. Math. Soc. 75 (1969), 1326-1329.
  • [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.
  • [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.
  • [5] P. Erdős, On integers of the form $2^k + p$ 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.
  • [11] Š. Porubský, Covering systems and generating functions, Acta Arith. 26 (1974/75), 223-231.
  • [12] Š. Porubský, On m times covering systems of congruences, Acta Arith. 29 (1976), 159-169.
  • [13] Š. Porubský, Results and problems on covering systems of residue classes, Mitt. Math. Sem. Giessen 1981, no. 150, 1-85.
  • [14] S. K. Stein, Unions of arithmetic sequences, Math. Ann. 134 (1958), 289-294.
  • [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.
  • [18] S. P. Tung, Complexity of sentences over number rings, SIAM J. Comp. 20 (1991), 126-143.
  • [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.
  • [21] Š. Znám, A survey of covering systems of congruences, Acta Math. Univ. Comenian. 40/41 (1982), 59-79.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-aav72i2p109bwm
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