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Is the sumset or the sumset of the square set always large?

A more general result than what you want appears as Theorem 1 in http://arxiv.org/pdf/1002.2554. (A slightly weaker result had appeared before as Theorem 3.1 in http://arxiv.org/pdf/0909.5471). Curio …
Boris Bukh's user avatar
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13 votes

Sumsets and dilates: does $|A+\lambda A|<|A+A|$ ever hold?

It is false. Let $\lambda$ be any integer other than $0$ and $\pm 1$. First, I will construct an example mod $p$ for every large prime $p$, which will then be upgraded to $\mathbb{Z}$ by taking Cartes …
Boris Bukh's user avatar
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