Download PDF - Covering the integers by arithmetic sequencesAll rights reserved. Copyright exceptions and limitations apply

ArticleOriginal scientific text

Title

Covering the integers by arithmetic sequences

Authors 1

Affiliations

  1. Department of Mathematics, Nanjing University, Nanjing 210093, People's Republic of China

Bibliography

  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 2k+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.
Acta Arithmetica
1995/72/2
Export to PBN, Opens in new tab
Pages:
109-129
Main language of publication
English
Received
1993-11-18
Accepted
1994-08-23
Published
1995
Exact and natural sciences