MathNet 2015-part-04 — 191 problems (EN–VI) Question 28

Let $a \ge 1$ and $b \ge 2$ be given positive integers. Show that there does not exist any non-constant polynomial $f(x)$ with integer coefficients such that $f(n^a)$ and $f(b^n)$ are relatively prime for every positive integer $n$.

(Battsengel B., Bayarmagnai G.)