MathDB

Let

c \ge 1

be a real number. Let

G

be an Abelian group and let

A \subset G

be a finite set satisfying

|A+A| \le c|A|

, where

X+Y:= \{x+y| x \in X, y \in Y\}

and

|Z|

denotes the cardinality of

Z

. Prove that

|\underbrace{A+A+\dots+A}_k| \le c^k |A|

for every positive integer

k

.
Proposed by Przemyslaw Mazur, Jagiellonian University.

Problem Statement