On the equation ${\mathbf{n}}_1{\mathbf{n}}_2={\mathbf{n}}_3{\mathbf{n}}_4$ restricted to factor closed sets

Sanying Shi, Michel Weber

We study the number of solutions $N(B,F)$ of the diophantine equation $n_1{n}_2=n_3{n}_4$, where $1\le n_1\le B$, $1\le n_3\le B$, $n_2,n_4\in F$ and $F\subset [1,B]$ is a factor clos…