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)
Further characterizations and properties of exactly covering congruences
โ Scribed by Aviezri S. Fraenkel
- Publisher
- Elsevier Science
- Year
- 1975
- Tongue
- English
- Weight
- 668 KB
- Volume
- 12
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
โฆ Synopsis
If ( 1) is an ECC, thepfl fibr ull i:n tegers n, c, r wtisjj&g n 0, 0 < r < c, where R,(x) is the nth = B, (0) is the rtth Bernoulli rzumbet. Con-&y, kt c be any positive integer. If (3) holds fur UN n 3 , . . . . c--1, then (I) isan ECC. e case c = I of this theorem was proved in [ 2). if (1) is un ECC, then c (__r,b:,;-1 'fj, iES2 .
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