𝔖 Bobbio Scriptorium
✦   LIBER   ✦

On disjoint residue classes

✍ Scribed by Zhi-Wei Sun

Book ID
103060188
Publisher
Elsevier Science
Year
1992
Tongue
English
Weight
310 KB
Volume
104
Category
Article
ISSN
0012-365X

No coin nor oath required. For personal study only.

✦ Synopsis

Sun, Z.-W., On disjoint residue classes, Discrete Mathmatics 104 (1992) 321-326. The purpose of this note is to show that, if n,, . , nk are positive integers, and for each d E Z+ satisfying f(d) G k -2 or a weaker condition d ~2~~~ (where f(d) = CI=, a,@, -1) if fl:=, p? is the prime factorization of d), the number of pairs {i, j} (1 G i <j c k) with gcd (n,, n,) = d is less than Vm, then there exist integers a,, , ak such that the residue classes a,(modn,),

, a,(modn,) are pairwise disjoint. We conjecture that m can be replaced by 2d -1.

πŸ“œ SIMILAR VOLUMES

On discount residue classes
On discount residue classes
✍ A.P. Huhn; L. Megyesi πŸ“‚ Article πŸ“… 1982 πŸ› Elsevier Science 🌐 English βš– 346 KB

It is shown that, whenever ml, m2, . . . , m, are natural numbers such that th: pairwise greatest common divisors, d, = (mi, mj), i # j are distinct anti different from 1, then there exist integers a,, a2, . . . , a,, such that the solution sets of the congruences x = ai (mod m,), i = 1.2,..., n are

Units in residue classes
Units in residue classes
✍ W. Narkiewicz πŸ“‚ Article πŸ“… 1988 πŸ› Springer 🌐 English βš– 263 KB
Two theorems on the addition of residue
Two theorems on the addition of residue classes
✍ David R. Guichard πŸ“‚ Article πŸ“… 1990 πŸ› Elsevier Science 🌐 English βš– 445 KB

It is well known that if a,, . , a, are residues module n and m an then some sum ai, + . . .+q,, iI<...<&, is 0 (mod n). In recent related work, Sydney Bulman-Fleming and Edward T.H. Wang have studied what they call n-divisible subsequences of a finite sequence u, and made a number of conjectures. W