5 problems

Let $v_p$ denote the $p$-adic valuation. The variables $x$ and $q$ are integers with $x>1$, and $p$ and $q$ are primes in the second assertion. Sharp upper-bound conjecture for Fer…

Let $p$ range over primes, let $v_p$ denote the $p$-adic valuation, and fix an integer $x>1$. Finiteness conjecture for exceptional Fermat quotients. The inequality … occurs for on…

Double-discriminant constant conjecture. The following hold:

Rowland–Yassawi's conjecture. For each $p\in\{31,37,61\}$ and every $n\in\mathbb{Z}_{\geq 0}$,

Let $G$ and $H$ be finite groups, and let $p$ be a prime. Write $v_p$ for the $p$-adic valuation, and let $C_G$ be a constant depending on $G$. Asymptotically, $o(1)$ denotes a qua…