RationalRootTheorem USAMTS Difficult
2018

Problem - 4271

Find, with proof, all ordered pairs of positive integers $(a, b)$ with the following property: there exist positive integers $r$, $s$, and $t$ such that for all $n$ for which both sides are defined, $$\binom{\binom{n}{a}}{b}=r\binom{n+s}{t}$$

The solution for this problem is available for $0.99. You can also purchase a pass for all available solutions for$99.