3 problems

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 $N$.

Let $d\geq 2$, and let $f\in \mathbb{Q}(z)_d$ be a rational function of degree $d$. The rational periodic points of $f$ are the points in $\mathbb{Q}$ that satisfy $f^k(z)=z$ for s…