On a conjecture of Graham on the p-divisibility of central binomial coefficients

Ernie Croot, Hamed Mousavi, Maxie Schmidt

We show that for every $r\ge 1$, and all $r$ distinct (sufficiently large) primes $p_1,...,p_r>p_0(r)$, there exist infinitely many integers $n$ such that $\left(\genfrac{}{}{0ex}{}{2n}{n}\right)$ is…