MathNet 2015-part-01 — 191 problems (EN–VI) Question 42

Let $m$, $n$ be positive integers and $a$, $b$ be positive real numbers different from $1$. Suppose that $m \gt n$ and $\frac{a^{m+1}-1}{a^m-1} = \frac{b^{n+1}-1}{b^n-1} = c$. Show that $a^m c^n \gt b^n c^m$.