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**9**

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603 views

### Cliques in the Paley graph and a problem of Sarkozy

The following question is motivated by pure curiosity; it is not a part
of any research project and I do not have any applications. The question
comes as an interpolation between two notoriously ...

**4**

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98 views

### Restricted addition analogue of Freiman's $(3n-4)$-theorem

There is a well-known theorem of Freiman saying that if $A$ is a finite set of integers with $|2A| \le 3|A|-4$, then $A$ is contained in an arithmetic progression with at most $|2A|-|A|+1$ terms. Is ...

**3**

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157 views

### Subgroup cliques in the Paley graph

It is a famous open problem to estimate non-trivially, for a prime $p\equiv 1\pmod 4$, the largest size of a subset $A\subset{\mathbb F}_p$ such that the difference of any two elements of $A$ is a ...

**2**

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135 views

### Doubling for Sumset of the same set

Let $G$ ($G=\mathbb{Z}^n_2$ for my case) be a additive group and $A$ be a subset of $G$. For any set $S\subseteq G$ define its doubling as $$\sigma (S)=\dfrac{|S+S|}{|S|}$$
Suppose $A$ has small ...

**1**

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52 views

### $B_k[1]$ sets with smallest possible $m = max B_k[1]$ for given $k$ and $n = |B_k[1]|$ elements

Sidon sets are sets $A \subset \mathbb{N}$ such that for all $a_j,b_j \in A$ holds
$$a_1+a_2=b_1+b_2 \iff \{a_1,a_2\}=\{b_1,b_2\}$$
Thus if you know the sum of two elements, you know which elements ...

**0**

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40 views

### When does the equality hold in Dias da Silva - Hamidoune Theorem?

Let $p$ be prime number and let $A$ be a $k$-elements subset of $\mathbb{Z}/p\mathbb{Z}$. Dias da Silva - Hamidoune Theorem states that $|h^{\hat{}}A| \geq \min(p, hk -h^2 + 1)$, where $h$ is an ...

**0**

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75 views

### Distortion of the Hausdorff dimension of sums of Cantor sets under local scaling

The following question deals with possible distortion of the Hausdorff dimension of sums of Cantor sets as one "zooms in" on the sum around any given point.
Let us assume that $C_1$ and $C_2$ are two ...