MathNet 2024-part-03 — 168 problems (EN–VI) Question 39

Find all real numbers $a, b \gt 1$ such that there are polynomials $P(x)$ and $Q(x)$ with real coefficients such that $P(x) \in \{a^n \mid n = 1, 2, \dots\}$ if and only if $Q(x) \in \{b^n \mid n = 1, 2, \dots\}$.