10 problems

Let $f(t)$ be an irreducible polynomial of degree at least $4$. For $N>0$, consider integers $t\in[N,2N]$ for which $f(t)$ is divisible by the square of a prime larger than…

ABC conjecture. For every $cepsilon>0$,

Folklore conjecture. One has

Square-free values asymptotic conjecture. There is a positive constant

Let $f(X)\in\mathbb{Z}[X]$ be a separable polynomial, and let $m\geq 2$ be an integer. Say that $f$ has no local obstruction for $m$th-power-free values if, for every prime $p$, th…

Let $a$, $b$, and $c$ be pairwise relatively prime positive integers satisfying … For a real number $\varepsilon>0$, let $C(\varepsilon)>0$ be a constant. The abc-conjecture. For e…

Let $f\in\mathbb{Z}[x]$ be a square-free polynomial, meaning that it has no nonconstant square divisor. Excluding some simple exceptional cases, the square-free values conjecture.…

Square-free values density conjecture. As $x\to\infty$,

Square-free values conjecture. There are infinitely many primes $p$ such that $f(p)$ is square-free.

Let … This counts triples in dyadic ranges for which $e^2f-1$ is a square. Square-root order conjecture. The true order of magnitude of $\mathcal{M}(E,F)$ might be about … The heur…