Exact m-covers and the linear form $∑^k_{s=1} x_s/n_s$

Zhi-Wei Sun

Exact m-covers and the linear form

\sum_{s = 1}^{k} x_{s} / n_{s}

Zhi-Wei Sun

Acta Arithmetica, Tome 80 (1997), p. 175-198 / Harvested from The Polish Digital Mathematics Library

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Publié le : 1997-01-01
EUDML-ID : urn:eudml:doc:207060

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     author = {Zhi-Wei Sun},
     title = {Exact m-covers and the linear form $$\sum$^k\_{s=1} x\_s/n\_s$
            },
     journal = {Acta Arithmetica},
     volume = {80},
     year = {1997},
     pages = {175-198},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-aav81i2p175bwm}
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Zhi-Wei Sun. Exact m-covers and the linear form $∑^k_{s=1} x_s/n_s$
            . Acta Arithmetica, Tome 80 (1997) pp. 175-198. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-aav81i2p175bwm/

Bibliographie

[000] [E] P. Erdős, On integers of the form $2^{k} + p$ and some related problems, Summa Brasil. Math. 2 (1950), 113-123. MR 13, 437.

[001] [GLS] A. Granville, S.-G. Li and Q. Sun, On the number of solutions of the equation $\sum_{i = 1}^{n} x_{i} / d_{i} \equiv 0 (m o d 1)$ , and of diagonal equations in finite fields, J. Sichuan Univ. (Nat. Sci. Ed.) 32 (3) (1995), 243-248.

[002] [Gu] R. K. Guy, Unsolved Problems in Number Theory, 2nd ed., Springer, New York, 1994, Sections F13 and F14.

[003] [LN] R. Lidl and H. Niederreiter, Finite Fields, Encyclopedia Math. Appl., 20, Addison-Wesley, 1983, 291-293. MR 86c:11106.

[004] [P] Š. Porubský, On m times covering systems of congruences, Acta Arith. 29 (1976), 159-169. MR 53#2884. | Zbl 0282.10033

[005] [Sm] C. Small, Diagonal equations over large finite fields, Canad. J. Math. 36 (1984), 249-262. MR 86e:11094.

[006] [SW] Q. Sun and D.-Q. Wan, On the Diophantine equation $\sum_{i = 1}^{n} x_{i} / d_{i} \equiv 0 (m o d 1)$ , Proc. Amer. Math. Soc. 112 (1991), 25-29. MR 91h:11017.

[007] [SWM] Q. Sun, D.-Q. Wan and D.-G. Ma, On the equation $\sum_{i = 1}^{n} y_{i} / d_{i} \equiv 0 (m o d 1)$ , J. Sichuan Univ. (Nat. Sci. Ed.) 23 (4) (1986), 25-30. MR 88e:11121.

[008] [Su1] Z. W. Sun, A necessary and sufficient condition for two linear diophantine equations to have a common solution, J. Nanjing Univ. (Nat. Sci. Ed.) 25 (1) (1989), 10-17. MR 90i:11026.

[009] [Su2] Z. W. Sun, On exactly m times covers, Israel J. Math. 77 (1992), 345-348. MR 93k : 11007. | Zbl 0768.11001

[010] [Su3] Z. W. Sun, Covering the integers by arithmetic sequences, Acta Arith. 72 (1995), 109-129. | Zbl 0841.11011

[011] [Su4] Z. W. Sun, Covering the integers by arithmetic sequences II, Trans. Amer. Math. Soc. 348 (1996), 4279-4320. | Zbl 0884.11013