AbstractFor integers a and n>0, let a(n) denote the residue class {x∈Z:x≡a(modn)}. Let A be a collection {as(ns)}s=1k of finitely many residue classes such that A covers all the integers at least m times but {as(ns)}s=1k−1 does not. We show that if nk is a period of the covering function wA(x)=|{1⩽s⩽k:x∈as(ns)}| then for any r=0,…,nk−1 there are at least m integers in the form ∑s∈I1/ns−r/nk with I⊆{1,…,k−1}
AbstractIf A is a set of positive integers, we denote by p(A,n) the number of partitions of n with p...
In the first chapter we investigate matters regarding the period of continued fractions of real numb...
AbstractTextPaul Erdős, in 1950, asked whether for each positive integer N there exists a finite set...
AbstractFor integers a and n>0, let a(n) denote the residue class {x∈Z:x≡a(modn)}. Let A be a collec...
AbstractLet {as(modns)}s=1k(k>1) be a finite system of residue classes with the moduli n1,…,nk disti...
AbstractA residue class a+nZ with weight λ is denoted by 〈λ,a,n〉. For a finite system A={〈λs,as,ns〉}...
AbstractConsider all the integers not exceeding x with the property that in the system number to bas...
be a finite system of congruence classes. We refer to n as the modulus of the congruence class a (mo...
AbstractM. Filaseta, K. Ford, S. Konyagin, C. Pomerance and G. Yu proved that if the reciprocal sum ...
AbstractThe group of units in the ring Zm of residue classes modm consists of the residues amodm wit...
Let Ω(n) denote the number of prime divisors of n counting multiplicity. One can show that for any p...
Introduction. Let k be a positive integer and F(x, k) denote the number of integers n < x which h...
ements. We will see in a moment that it is possible to do some arithmetic with these elements. Thin...
AbstractA setAof non-negative integers is aSidon setif the sumsa+b(a,b∈A,a⩽b) are distinct. Assume t...
In this paper, we study necessary conditions for small sets of congruences with distinct moduli to c...
AbstractIf A is a set of positive integers, we denote by p(A,n) the number of partitions of n with p...
In the first chapter we investigate matters regarding the period of continued fractions of real numb...
AbstractTextPaul Erdős, in 1950, asked whether for each positive integer N there exists a finite set...
AbstractFor integers a and n>0, let a(n) denote the residue class {x∈Z:x≡a(modn)}. Let A be a collec...
AbstractLet {as(modns)}s=1k(k>1) be a finite system of residue classes with the moduli n1,…,nk disti...
AbstractA residue class a+nZ with weight λ is denoted by 〈λ,a,n〉. For a finite system A={〈λs,as,ns〉}...
AbstractConsider all the integers not exceeding x with the property that in the system number to bas...
be a finite system of congruence classes. We refer to n as the modulus of the congruence class a (mo...
AbstractM. Filaseta, K. Ford, S. Konyagin, C. Pomerance and G. Yu proved that if the reciprocal sum ...
AbstractThe group of units in the ring Zm of residue classes modm consists of the residues amodm wit...
Let Ω(n) denote the number of prime divisors of n counting multiplicity. One can show that for any p...
Introduction. Let k be a positive integer and F(x, k) denote the number of integers n < x which h...
ements. We will see in a moment that it is possible to do some arithmetic with these elements. Thin...
AbstractA setAof non-negative integers is aSidon setif the sumsa+b(a,b∈A,a⩽b) are distinct. Assume t...
In this paper, we study necessary conditions for small sets of congruences with distinct moduli to c...
AbstractIf A is a set of positive integers, we denote by p(A,n) the number of partitions of n with p...
In the first chapter we investigate matters regarding the period of continued fractions of real numb...
AbstractTextPaul Erdős, in 1950, asked whether for each positive integer N there exists a finite set...
DOI
Add to ORKG