AbstractLet {as(modns)}s=1k(k>1) be a finite system of residue classes with the moduli n1,…,nk distinct. By means of algebraic integers we show that the range of the covering function w(x)=|{1⩽s⩽k:x≡as(modns)}| is not contained in any residue class with modulus greater one. In particular, the values of w(x) cannot have the same parity
Since their introduction by Erdős in 1950, covering systems (that is, finite collections of arithmet...
26 pages, accepté pour publication dans le journal Functiones et approximatioInternational audienceL...
The work in this thesis is based on a paper written by Bob Hough in 2013. This thesis addresses the ...
AbstractFor integers a and n>0, let a(n) denote the residue class {x∈Z:x≡a(modn)}. Let A be a collec...
AbstractM. Filaseta, K. Ford, S. Konyagin, C. Pomerance and G. Yu proved that if the reciprocal sum ...
AbstractA famous unsolved conjecture of P. Erdős and J.L. Selfridge states that there does not exist...
A covering system is a finite collection of arithmetic progressions whose union is the set of intege...
be a finite system of congruence classes. We refer to n as the modulus of the congruence class a (mo...
AbstractConsider all the integers not exceeding x with the property that in the system number to bas...
A covering system or a covering is a set of linear congruences such that every integer satisfies at ...
AbstractTextPaul Erdős, in 1950, asked whether for each positive integer N there exists a finite set...
In this paper, we study necessary conditions for small sets of congruences with distinct moduli to c...
In 1950 Paul Erdos observed that every integer belonged to a certain system of congruences with dist...
Covering systems were introduced by Erd\H{o}s in 1950. In the same article where he introduced them,...
A covering system of the integers is a finite system of congruences where each integer satisfies at ...
Since their introduction by Erdős in 1950, covering systems (that is, finite collections of arithmet...
26 pages, accepté pour publication dans le journal Functiones et approximatioInternational audienceL...
The work in this thesis is based on a paper written by Bob Hough in 2013. This thesis addresses the ...
AbstractFor integers a and n>0, let a(n) denote the residue class {x∈Z:x≡a(modn)}. Let A be a collec...
AbstractM. Filaseta, K. Ford, S. Konyagin, C. Pomerance and G. Yu proved that if the reciprocal sum ...
AbstractA famous unsolved conjecture of P. Erdős and J.L. Selfridge states that there does not exist...
A covering system is a finite collection of arithmetic progressions whose union is the set of intege...
be a finite system of congruence classes. We refer to n as the modulus of the congruence class a (mo...
AbstractConsider all the integers not exceeding x with the property that in the system number to bas...
A covering system or a covering is a set of linear congruences such that every integer satisfies at ...
AbstractTextPaul Erdős, in 1950, asked whether for each positive integer N there exists a finite set...
In this paper, we study necessary conditions for small sets of congruences with distinct moduli to c...
In 1950 Paul Erdos observed that every integer belonged to a certain system of congruences with dist...
Covering systems were introduced by Erd\H{o}s in 1950. In the same article where he introduced them,...
A covering system of the integers is a finite system of congruences where each integer satisfies at ...
Since their introduction by Erdős in 1950, covering systems (that is, finite collections of arithmet...
26 pages, accepté pour publication dans le journal Functiones et approximatioInternational audienceL...
The work in this thesis is based on a paper written by Bob Hough in 2013. This thesis addresses the ...