3 problems

Let $[x]_q$ denote the $q$-deformation of a real number $x>0$, viewed as a power series in the complex variable $q$, and let $R(x)$ be its radius of convergence. For the golden rat…

Let $N$ be an integer greater than $2$, and let the size of an irreducible solution of $(E_N)$ mean the size notion defined earlier in the paper. Uniform size-bound conjecture. The…

Let $N\in\mathbb{N}^{*}$ with $N\geq 2$. A solution of $(E_N)$ is called irreducible when it cannot be decomposed as a sum of two nontrivial solutions, as in the preceding discussi…