Prime power divisors of binomial coefficients Original Research Article

It is known that for sufficiently large n and m and any r the binomial coefficient (nm) which is close to the middle coefficient is divisible by pr where p is a ‘large’ prime. We prove the exact divisibility of (nm) by pr for p > c(n). The lower bound is essentially the best possible. We also prove some other results on divisibility of binomial coefficients.