MathNet 2015-part-04 — 191 problems (EN–VI) Question 36

Given are positive integers $r$ and $k$ and an infinite sequence of positive integers $a_{1} \leq a_{2} \leq \ldots$ such that $\frac{r}{a_{r}}=k+1$. Prove that there exists a $t$ with $\frac{t}{a_{t}}=k$.