9 problems

Let $q=19^3$, let … and let $[5]=T^{q^5}-T$ and $M_5$ be Thakur's polynomial. The polynomial $P\in\mathbf{F}_{19^3}[T]$ is the degree-five $c$-Wieferich prime exhibited in the pape…

Let $A$ be the polynomial ring in the paper, let $\phi$ be the given Drinfeld module, and let $a\in A$ be the fixed base. A polynomial has no square factors when it is squarefree, a…

Let $E/\mathbb{Q}$ be an elliptic curve and let $P\in E^0(\mathbb{Q})$ be a non-torsion point. Define the sets of good primes … and $W_{E,P}$ as the set of primes for which…

A prime $p$ is non-Wieferich if there is an integer $N$ for which $N^{p-1}\not\equiv1\pmod{p^2}$. Infinitude conjecture for non-Wieferich primes. There exist infinitely many non-Wi…

Infinitude conjecture for $\mu$-hits. There are infinitely many $\mu$-hits.

Let $p<q$ be primes. A pair $(p,q)$ is called a Wieferich pair when it satisfies the paper's Wieferich condition. Wieferich-free two-prime $S$-Diophantine quadruple conjecture. If…

Let $p<q$ be primes. A pair $(p,q)$ is called a Wieferich pair when it satisfies the paper's Wieferich condition. Wieferich-free two-prime $S$-Diophantine quadruple conjecture. If…

Let $X=\{a_1,\ldots,a_m\}$ be a finite set of algebraic numbers, and let $K$ be a number field containing all $a_i$. An $X$-base Fibonacci-Wieferich prime is a prime ideal…

Let $A=\mathbb{F}_q[T]$ have characteristic $p$, and let a Wieferich prime in $A$ mean a prime satisfying the Wieferich condition discussed in the paper. Thakur's conjecture. For e…