Let $A$ be a finite set of integers. We show that if $k$ is a prime power or a product of two distinct primes then \[ |A+k\cdot A|\geq(k+1)|A|-\lceil k(k+2)/4\rceil \] provided $|A|\geq (k-1)^{2}k!$, where $A+k\cdot A=\{a+kb:\ a,b\in A\}$. We also establish the inequality $|A+4\cdot A|\geq5|A|-6 $ for $|A|\geq5$.
@article{10_37236_2801,
author = {Shan-Shan Du and Hui-Qin Cao and Zhi-Wei Sun},
title = {On a sumset problem for integers},
journal = {The electronic journal of combinatorics},
year = {2014},
volume = {21},
number = {1},
doi = {10.37236/2801},
zbl = {1308.11010},
url = {http://geodesic.mathdoc.fr/articles/10.37236/2801/}
}
TY - JOUR
AU - Shan-Shan Du
AU - Hui-Qin Cao
AU - Zhi-Wei Sun
TI - On a sumset problem for integers
JO - The electronic journal of combinatorics
PY - 2014
VL - 21
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.37236/2801/
DO - 10.37236/2801
ID - 10_37236_2801
ER -
%0 Journal Article
%A Shan-Shan Du
%A Hui-Qin Cao
%A Zhi-Wei Sun
%T On a sumset problem for integers
%J The electronic journal of combinatorics
%D 2014
%V 21
%N 1
%U http://geodesic.mathdoc.fr/articles/10.37236/2801/
%R 10.37236/2801
%F 10_37236_2801
Shan-Shan Du; Hui-Qin Cao; Zhi-Wei Sun. On a sumset problem for integers. The electronic journal of combinatorics, Tome 21 (2014) no. 1. doi: 10.37236/2801
