Title: Équations en diviseurs

Abstract: Let $d(n) \subset \mathbb{N}$ be the set of the $\tau(n)$ divisors of $n$. We generalize a method of Tenenbaum and de la Bret\`eche for the study of the set $d(n)$. Among other things, we establish that $$ |\{(d_1,d_2,d_3) \in d(n)^3 : d_1+d_2=d_3\}| \le \tau(n)^{2-\delta} $$ with $\delta=0.045072$.