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1
vote
Accepted
Unique representation and sumsets
One can have $|2A|$ as small as $2|A|$. Take $A = H \cup \{g\}$ where $H$ is a subgroup, $g \notin H$ and$g \neq -g$. Then $|A+A| = 2|A| + O(1)$ while
$g+H$ and $H - g$ all have a unique representati …
10
votes
Accepted
Sidon sets of $\mathbb{Z}/p\mathbb{Z}$
I am not sure of your level of knowledge of Sidon sets, but a good reference is O' Bryant's survey (see section 4.3 in particular) which contains several constructions in the integers. If you are alre …