We show that for any relatively prime integers $1\leq p q$ and for any finite $A \subset \mathbb {Z}$ one has $$|p \cdot A + q \cdot A | \geq (p + q) |A| - (pq)^{(p+q-3)(p+q) + 1}.$$
Keywords:
relatively prime integers leq finite subset mathbb has cdot cdot geq q
Affiliations des auteurs :
Antal Balog
1
;
George Shakan
2
1
Alfréd Rényi Institute of Mathematics P.O. Box 127 1364 Budapest, Hungary
2
Department of Mathematics University of Wyoming Laramie, WY 82072, U.S.A.
@article{10_4064_aa164_2_5,
author = {Antal Balog and George Shakan},
title = {On the sum of dilations of a set},
journal = {Acta Arithmetica},
pages = {153--162},
year = {2014},
volume = {164},
number = {2},
doi = {10.4064/aa164-2-5},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/aa164-2-5/}
}
TY - JOUR
AU - Antal Balog
AU - George Shakan
TI - On the sum of dilations of a set
JO - Acta Arithmetica
PY - 2014
SP - 153
EP - 162
VL - 164
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UR - http://geodesic.mathdoc.fr/articles/10.4064/aa164-2-5/
DO - 10.4064/aa164-2-5
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%A Antal Balog
%A George Shakan
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%J Acta Arithmetica
%D 2014
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%V 164
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4064/aa164-2-5/
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Antal Balog; George Shakan. On the sum of dilations of a set. Acta Arithmetica, Tome 164 (2014) no. 2, pp. 153-162. doi: 10.4064/aa164-2-5
