5 problems

Let $m$ be a positive odd integer, and define … Here $S_{n,2}(d,p)$ is the determinant considered in the paper. Sun's finiteness conjecture. For every positive odd integer $m$, the…

Derangement factorial-sum conjecture. For every prime number $p>11$,

Let $C(n)$ range over the Apéry-like sequences listed in Tables 2 and 3 of the source, including $(\eta)$ and the sequences $(\delta)$, $(\alpha)$, $(\epsilon)$, $(\zeta)$, and…

Let $A(n)$ denote the Apéry numbers, and let a prime divide the sequence if it divides at least one term $A(n)$. The Apéry-number proportion conjecture. The proportion of primes th…

Bruckman–Anderson conjecture. If $m=q^e$ is a prime power with $e\geq 1$, then