Prime power divisors of binomial coefficients
This excellent paper provides \textit{asymptotic} bounds for the number of primes \(p\) such that \(p^r\|\binom{n}{m}\), when \(n\) goes to infinity and \(m\) is larger than some power of \(n\). The uniformity in \(r\) is furthermore carried out. The method is deceptively simple looking and relies on a lemma (Lemma~3) of great generality that gives a Vinogradov type bound for exponential sums over primes, a lemma which is worth looking at on its own.
scientific article; zbMATH DE number 1334444
scientific article