When is ${\displaystyle \scriptstyle {N \choose K}}$divisible by P ? — 79.115.135.150 (talk) 23:11, 7 December 2013 (UTC)[reply]

See Lucas' theorem for one criterion. (This actually implies a pattern in Pascal's triangle modulo p that looks like a Sierpinski's triangle where at each stage you subdivide by p instead of 2.) Sławomir Biały (talk) 14:00, 8 December 2013 (UTC)[reply]