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A simple characterization of disjoint covering systems

✍ Scribed by Štefan Znám

Publisher
Elsevier Science
Year
1975
Tongue
English
Weight
288 KB
Volume
12
Category
Article
ISSN
0012-365X

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✦ Synopsis

a system of arithmetic sequences to ith 0 G a < ?I. y a(n) dGnote the set of all where s is an teger. A system . If(f)isa S, then putting z = -1 in (3) we get ~ll~~xP[~~l -'. 1) + eee + ~xp[~~]/(exp[~~] -11) = l/(e -1).

ow the opp,osi te is sbvious.

in [2] that (1) is

📜 SIMILAR VOLUMES

A characterization of exactly covering c
A characterization of exactly covering congruences
✍ Aviezri S. Fraenkel 📂 Article 📅 1973 🏛 Elsevier Science 🌐 English ⚖ 454 KB

If every nonnegative integer occurs in exactly one of the integer sequences QiU+$, It = 0, 1,2, . . . . 0 < 41 (... Lam, 0 5 bi < aj, i = 1, . . . . m, then the system ain + bi is called an exactly covering system (ECS). Our main result is that ain f bi is an ECS if and only if I%! \_ ape1 B,(bi/ai)