3 problems

Let $\phi(x)=x^2+c$ for some $c\in\mathbb{Q}$, and let $a\in\mathbb{Q}$ be a periodic point for $\phi$, meaning that $\phi^n(a)=a$ for some $n\geq1$; the least such $n$ is the peri…

Let $f_c(x)=x^2+c\in\mathbb{Q}[x]$ be a quadratic polynomial, and let a rational point have exact period $n$ if its period is $n$ and no smaller positive period. Uniform Boundednes…

Flynn–Poonen conjecture. There is no quadratic polynomial $f(x)\in{\mathbb Q}[x]$ with a rational point of exact period $N$.