2 problems

Let $A\subset\mathbb{R}$ be a finite set. If $\xi\in\mathbb{R}$ is transcendental and $K_1,K_2\geqslant 2$ satisfy … then The real polynomial Freiman-Ruzsa conjecture. … This conje…

Let $p$ be a prime, and let $\phi:\mathbb{F}_p^n\to\mathbb{F}_p^N$ be a function such that $\phi(x+y)-\phi(x)-\phi(y)$ takes values in a set $S$. Let $K$ be the doubling parameter…