11 problems

Let $(a,b,c)$ be an admissible triplet, meaning a triplet of positive integers satisfying the admissibility conditions for the three-variable Frobenius problem, and let $f(a,b,c)$…

Let $a$ be an integer with $a>30$, and let … Let $S(A(a))$ be the numerical semigroup generated by $A(a)$. For $n\in\mathbb{Z}^{+}$, let $\iota(n)$ be the least number of positive…

Let $g(k)$ be the least positive integer such that for every pair of integers satisfying $g(k)<a_1<a_2$, there is a prime power $p^k\le g_{a_1,a_2}$ of the form $p^k=a_1x+a_2y$ wit…

Let $a_1$ and $a_2$ be integers with $a_2>a_1>40$ and $\gcd(a_1,a_2)=1$. Let $\pi_{2,a_1,a_2}$ denote the number of prime squares $p^2\le g_{a_1,a_2}$ representable as…

Unboundedness conjecture. For every positive integer $m\geqslant 1$, there exists some $\alpha\in\mathfrak{O}_K^+$ such that

Let $1<c<d$ be relatively prime integers and set … Let $\pi_{c,d}$ denote the number of primes not exceeding $g_{c,d}$ that can be written as $cx+dy$ with…

Let $s\ge 3$. Let $a_k$, where $k\in [s]$, be positive integers such that $(a_1,a_2,\ldots,a_s)=1$. Then $S_{s,s-2}^m(a_1,a_2,\ldots,a_s)$ denotes the set of positive integers sati…

Parametric relation-set conjecture. There exists a PILP whose lattice point set equals $G(S(t))$ for $t\gg0$. The same is true for

Roune–Woods conjecture. The function $D$ is an eventual quasi-polynomial (EQP).

Let $a_i:bbZ_+crightarrowbbZ_+$, $1cle icle n$, be eventually positive functions in $cmathrm{EQP}$, where $F(a_1,\cdots,a_n)$ denotes the largest element of the group…

Let $\Lambda$ be a numerical semigroup, meaning a cofinite subsemigroup of the non-negative integers. Let $e(\Lambda)$ be the size of its minimal generating set, let…