Sur les coefficients du binôme (Q2559403)

The author shows that the binomial coefficient \(\binom nm\) divides the least common multiple of \(n, n-1, \dots, n-m+1\) for all natural numbers \(n,m\) with \(n\geq m\). As consequences of this result he shows that \(\binom nm\) is not a prime power for \(km<n-1\), and for \(n>m+m!\). The number \(\binom nm\) has at most \(m\) distinct prime divisors.