Unsolved Problems

Let $p>q\geq 2$ be two coprime integers. We call $n$ representable if it is the sum of integers of the form $p^kq^l$, none of which divide each other....

If $G$ is a finite graph and $A,B$ are disjoint sets of vertices then we call $A,B$ anticomplete if there are no edges between $A$ and $B$. If $t,c\ge...

Let $1\leq d_1<d_2$ and $k\geq 3$. Does there exist an integer $r$ such that if $B=\{b_1<\cdots\}$ is a lacunary sequence of positive integers with $b...

A positive odd integer $m$ such that none of $2^km+1$ are prime for $k\geq 0$ is called a Sierpinski number. We say that a set of primes $P$ is a cove...

Let $f(z)$ be an entire function which is not a monomial. Let $ u(r)$ count the number of $z$ with $\lvert z\rvert=r$ such that $\lvert f(z)\rvert=\ma...

Let $f\in \mathbb{C}[z]$ be a monic polynomial of degree $n$, all of whose roots satisfy $\lvert z\rvert\leq 1$. Let $ E= \{ z : \lvert f(z)\rvert \le...

Let $f:\mathbb{N}\to \mathbb{R}$ be an additive function (i.e. $f(ab)=f(a)+f(b)$ whenever $(a,b)=1$). Let $ A=\{ n \geq 1: f(n+1)< f(n)\}. $ If $\lver...

For $x_1,\ldots,x_n\in [-1,1]$ let $ l_k(x)=\frac{\prod_{i eq k}(x-x_i)}{\prod_{i eq k}(x_k-x_i)}, $ which are such that $l_k(x_k)=1$ and $l_k(x_i)=0$...

For $x_1,\ldots,x_n\in [-1,1]$ let $ l_k(x)=\frac{\prod_{i eq k}(x-x_i)}{\prod_{i eq k}(x_k-x_i)}, $ which are such that $l_k(x_k)=1$ and $l_k(x_i)=0$...

For $x_1,\ldots,x_n\in [-1,1]$ let $ l_k(x)=\frac{\prod_{i eq k}(x-x_i)}{\prod_{i eq k}(x_k-x_i)}, $ which are such that $l_k(x_k)=1$ and $l_k(x_i)=0$...

For $x_1,\ldots,x_n\in [-1,1]$ let $ l_k(x)=\frac{\prod_{i eq k}(x-x_i)}{\prod_{i eq k}(x_k-x_i)}, $ which are such that $l_k(x_k)=1$ and $l_k(x_i)=0$...

Let $C>0$. There exists $\epsilon>0$ such that if $n$ is sufficiently large the following holds. For any $x_1,\ldots,x_n\in [-1,1]$ there exist $y_1,\...