Question 162
Let $a, b, c, d$ be positive integers such that only finite number of prime numbers divide at least one element of the set
$$
\{a \cdot b^n + c \cdot d^n : n = 1, 2, 3, \dots\}.
$$
Prove that $b = d$.
$$
\{a \cdot b^n + c \cdot d^n : n = 1, 2, 3, \dots\}.
$$
Prove that $b = d$.