5 problems

Let $t$ be a positive integer, let $S=\{x_1,x_2,\ldots,x_n\}$ be a GCD-closed set of positive integers, and let the power LCM matrix be the matrix … The Hong conjecture. There exis…

Let $a$ and $b$ be positive integers with $a\mid b$, and let $S$ be a finite gcd-closed set of positive integers. For each $x\in S$, let $G_S(x)$ denote the set of greatest-type di…

Let $S=\{x_1,\ldots,x_n\}$ be an odd-GCD-closed set, and let $f$ be a completely multiplicative function, meaning $f(ab)=f(a)f(b)$ for positive integers $a,b$. If $f$ is strictly m…

Let $S=\{x_1,\ldots,x_n\}$ be an odd-GCD-closed set, meaning that $S$ consists of odd positive integers and is closed under greatest common divisors. For a real exponent $\alpha$,…

Let $S$ be a GCD-closed set of odd positive integers, meaning that every element of $S$ is odd and the greatest common divisor of any two elements of $S$ belongs to $S$. Let…