On the Multiplicative Properties Modulo $m$ of Numbers with Missing Digits

We obtain upper bounds for character sums modulo a composite number over sets of numbers with missing digits in a number system. We derive results on the solvability of congruences of the form $x_1\dotsb x_t\equiv\lambda\pmod{m}$ in the numbers with missing digits and also asymptotic formulas for the number of solutions.