All Questions

Let $p$ be a prime, let $A$ be a subset of $\mathbb{F}_p$, and let $v \in \mathbb{F}_p \setminus \{0\}$. Under what conditions is $|v \cdot A + A|$ (that is, $|\{ va + b : a \in A,\ b \in A \}|$) ...

1. Let $G$ be a finite group of order $n$. I need an estimate for the number $c$ of conjugacy classes of subgroups $D\subseteq G$. Note that any subgroup of $G$ contains $1_G$, and so the set of all ...

I consider two sequences of numbers: $A=\{a_1,...,a_{m-1},n\}$ and $B=\{n-a_{m-1},...,n-a_1,n\}$, where $a_1 < a_2 < ... < a_{m-1} < n$ and $\gcd(A) = \gcd(B) = 1$. I investigate the ...