11 citations · 29 across the 23 of their papers we have counts for
13 papers · 1 filter
On odd covering systems with distinct moduli
Song Guo, Zhi-Wei Sun
A famous unsolved conjecture of P. Erdos and J. L. Selfridge states that there does not exist a covering system {a_s(mod n_s)}_{s=1}^k with the moduli n_1,...,n_k odd, distinct and…
Groups and Combinatorial Number Theory
Zhi-Wei Sun
In this talk we introduce several topics in combinatorial number theory which are related to groups; the topics include combinatorial aspects of covers of groups by cosets, and als…
A connection between covers of the integers and unit fractions
Zhi-Wei Sun
For integers a and n>0, let a(n) denote the residue class {x\in Z: x=a (mod n)}. Let A be a collection {a_s(n_s)}_{s=1}^k of finitely many residue classes such that A covers all th…
On various restricted sumsets
Zhi-Wei Sun, Yeong-Nan Yeh
For finite subsets A_1,...,A_n of a field, their sumset is given by {a_1+...+a_n: a_1 in A_1,...,a_n in A_n}. In this paper we study various restricted sumsets of A_1,...,A_n with…
On Euler numbers modulo powers of two
Zhi-Wei Sun
To determine Euler numbers modulo powers of two seems to be a difficult task. In this paper we achieve this and apply the explicit congruence to give a new proof of a classical res…
On the range of a covering function
Zhi-Wei Sun
Let {a_s(mod n_s)}_{s=1}^k (k>1) be a finite system of residue classes with the moduli n_1,...,n_k distinct. By means of algebraic integers we show that the range of the covering f…