Question 24
Let $S=\{2i-1:i=1,2,\ldots,2019\}$. Determine the minimum value of $k$, where $k$ is a positive integer, such that for any subset $A$ of $S$ with $|A|\ge k$, $A$ contains two numbers $a,b$ with the property that $b=3^s a$ for some integer $s\ge1$.