On the difference between squares and integral $S$-units

Let $q_1,\dots ,q_t$ be distinct prime numbers. Let $a_1,\dots ,a_t$ be nonnegative integers and $x$ a positive integer. We establish an effective lower bound for the greatest prime divisor of $\mathrm{\mid }{x}^2-q_1^{a_1}\dots q_t^{a_t}\mathrm{\mid }$, which tends to infinity with the maximum of $x$, $a_1,\dots ,a_t$.