Binomial coefficients and the ring of p-adic integers

Zhi-Wei Sun, Wei Zhang

Let k>1 be an integer and let p be a prime. We show that if $p^a\le k<2p^a$ or $k=p^{a}q+1$ (with 2q<p) for some a=1,2,..., then the set {\binom{n}{k}: n=0,1,2,...} is dense in the r…