By system we mean a multi-set whose elements are unordered but may occur repeatedly. FollowingŠ. Znám [8] we use a(n) to denote the residue class { x ∈ Z : x ≡ a (mod n) }. For a system (1) A = {a i (n i)} k i=1 of residue classes, the n i are called its moduli. Definition. An integer T is said to be a covering period of (1) if it is a period of the characteristic function of the set k i=1 a i ...

We study integer partitions in which the parts fulfill the same congruence relations with the parts of their conjugates, called conjugate–congruent partitions. The results obtained include uniqueness criteria, weight lower-bounds and enumerating generating functions. © 2007 Elsevier B.V. All rights reserved. MSC: 11P81; 11P83; 05A15

Separations among the first-order logic Res(0,+,×) of finite residue classes, its extensions with generalized quantifiers, and in the presence of a built-in order are shown in this article, using algebraic methods from class field theory. These methods include classification of spectra of sentences over finite residue classes as systems of congruences, and the study of their h-densities over th...