Testwiki:Reference desk/Archives/Mathematics/2013 December 7

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December 7

When is N choose K divisible by P ?

When is $(\genfrac{}{}{0ex}{}{N}{K})$ divisible by P ? — 79.115.135.150 (talk) 23:11, 7 December 2013 (UTC)

Pascal's triangle modulo the prime number 7 for n less than 49.

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)