Powers in prime bases and a problem on central binomial coefficients

Sebastian Tim Holdum, Frederik Ravn Klausen, Peter Michael Reichstein Rasmussen

It is an open problem whether $\left(\genfrac{}{}{0ex}{}{2n}{n}\right)$ is divisible by 4 or 9 for all $n>256$. In connection with this, we prove that for a fixed uneven $m$ the asymptotic density of $k$'…