Baltic Way 1993 · Problem 2

Solution:

Let $a = 6$, $b = 3$ and denote $x_{n} = a n + b$. Then we have $x_{l} \cdot x_{m} = x_{6 l m + 3(l + m) + 1}$ for any natural numbers $l$ and $m$. Thus, any powers of the numbers $x_{n}$ belong to the same sequence.