AbstractA famous unsolved conjecture of P. Erdős and J.L. Selfridge states that there does not exist a covering system {as(modns)}s=1k with the moduli n1,…,nk odd, distinct and greater than one. In this paper we show that if such a covering system {as(modns)}s=1k exists with n1,…,nk all square-free, then the least common multiple of n1,…,nk has at least 22 prime divisors
The starting point for this work is the family of functions $\overline{p}_{-t}(n)$ which counts the ...
In 1950 Paul Erdos observed that every integer belonged to a certain system of congruences with dist...
AbstractIn this papar, the main results concern Natural Exactly Covering Systems (NECS's)(2) (i.e., ...
AbstractA famous unsolved conjecture of P. Erdős and J.L. Selfridge states that there does not exist...
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...
A conjecture made in 1849 by French mathematician Alphonse de Polignac is that every odd number can ...
AbstractThe expressions ϕ(n)+σ(n)−3n and ϕ(n)+σ(n)−4n are unusual among linear combinations of arith...
AbstractLet p be an odd prime and γ(k,pn) be the smallest positive integer s such that every integer...
AbstractIn this note, we supply the details of the proof of the fact that if a1,…,an+Ω(n) are intege...
A covering system is a finite collection of arithmetic progressions whose union is the set of intege...
AbstractM. Filaseta, K. Ford, S. Konyagin, C. Pomerance and G. Yu proved that if the reciprocal sum ...
AbstractBerger, Felzenbaum, and Fraenkel characterized all disjoint covering systems with precisely ...
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...
The starting point for this work is the family of functions $\overline{p}_{-t}(n)$ which counts the ...
In 1950 Paul Erdos observed that every integer belonged to a certain system of congruences with dist...
AbstractIn this papar, the main results concern Natural Exactly Covering Systems (NECS's)(2) (i.e., ...
AbstractA famous unsolved conjecture of P. Erdős and J.L. Selfridge states that there does not exist...
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...
A conjecture made in 1849 by French mathematician Alphonse de Polignac is that every odd number can ...
AbstractThe expressions ϕ(n)+σ(n)−3n and ϕ(n)+σ(n)−4n are unusual among linear combinations of arith...
AbstractLet p be an odd prime and γ(k,pn) be the smallest positive integer s such that every integer...
AbstractIn this note, we supply the details of the proof of the fact that if a1,…,an+Ω(n) are intege...
A covering system is a finite collection of arithmetic progressions whose union is the set of intege...
AbstractM. Filaseta, K. Ford, S. Konyagin, C. Pomerance and G. Yu proved that if the reciprocal sum ...
AbstractBerger, Felzenbaum, and Fraenkel characterized all disjoint covering systems with precisely ...
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...
The starting point for this work is the family of functions $\overline{p}_{-t}(n)$ which counts the ...
In 1950 Paul Erdos observed that every integer belonged to a certain system of congruences with dist...
AbstractIn this papar, the main results concern Natural Exactly Covering Systems (NECS's)(2) (i.e., ...
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