Covering the integers by arithmetic sequences

Zhi Wei Sun

Acta Arithmetica (1995)

  • Volume: 72, Issue: 2, page 109-129
  • ISSN: 0065-1036

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Zhi 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

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  1. [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. [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. [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. [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. [5] P. Erdős, On integers of the form 2 k + p and some related problems, Summa Brasil. Math. 2 (1950), 113-123. 
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  7. [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. [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. [9] R. K. Guy, Unsolved Problems in Number Theory, Springer, New York, 1981. 
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  13. [13] Š. Porubský, Results and problems on covering systems of residue classes, Mitt. Math. Sem. Giessen 1981, no. 150, 1-85. Zbl0479.10032
  14. [14] S. K. Stein, Unions of arithmetic sequences, Math. Ann. 134 (1958), 289-294. Zbl0084.04302
  15. [15] Z. W. Sun, Several results on systems of residue classes, Adv. in Math. (Beijing) 18 (1989), 251-252. 
  16. [16] Z. W. Sun, An improvement to the Znám-Newman result, Chinese Quart. J. Math. 6 (3) (1991), 90-96. 
  17. [17] Z. W. Sun, On exactly m times covers, Israel. J. Math. 77 (1992), 345-348. Zbl0768.11001
  18. [18] S. P. Tung, Complexity of sentences over number rings, SIAM J. Comp. 20 (1991), 126-143. Zbl0717.03002
  19. [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. [20] Š. Znám, On exactly covering systems of arithmetic sequences, Math. Ann. 180 (1969), 227-232. Zbl0169.37405
  21. [21] Š. Znám, A survey of covering systems of congruences, Acta Math. Univ. Comenian. 40/41 (1982), 59-79. 

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