Problem

Source: 2017 ELMO #4

Tags: number theory, ELMO 2017, Elmo



An integer $n>2$ is called tasty if for every ordered pair of positive integers $(a,b)$ with $a+b=n,$ at least one of $\frac{a}{b}$ and $\frac{b}{a}$ is a terminating decimal. Do there exist infinitely many tasty integers? Proposed by Vincent Huang