4 citations · 12 across the 20 of their papers we have counts for
13 papers · 1 filter
On value sets of polynomials over a field
Zhi-Wei Sun
Let F be any field. Let p(F) be the characteristic of F if F is not of characteristic zero, and let p(F)=+\infty otherwise. Let A_1,...,A_n be finite nonempty subsets of F, and let…
A sharp result on m-covers
Hao Pan, Zhi-Wei Sun
Let A={a_s+n_sZ}_{s=1}^k be a finite system of arithmetic sequences which forms an m-cover of Z (i.e., every integer belongs at least to m members of A). In this paper we show the…
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…
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 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…