All Questions

Fix some nonzero integers $a_1, \dots, a_k$, with $k \geq 2$, and some real numbers $c_1, \dots, c_k \in (0,1)$. For every positive integer $m$, let $N(m)$ be the number of $k$-tuple of integers $(x_1,...

For each prime $p$, let us define $$w_p:=|\{k^{k+1}+(k+1)^k\pmod p:\ k=0,\ldots,p-1\}|,$$ where $a\pmod p$ denotes the residue class $a+p\mathbb Z$. Based on my computation, I conjecture that $$w_p=...

Let $A$ be an $n\times n$ matrix with integer entries and let $d_1,...,d_n|q$ all be given natural numbers (I am happy to assume that $q$ is a prime power). How many solutions $x_1,...,x_n$ modulo $q$...

Given $n\in\Bbb N$ is there an $a_n\in\Bbb N$ such that for every $a>a_n$ there are two distinct integers $0<b<c<a$ such that $b^i\bmod a,c^i\bmod a\in(\sqrt a,\sqrt a\log a)$ for every $i\...