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If $p$ is a prime number and $r = 1,2,3 \dots ,p -1$, how can I prove that the binomial coefficients $_nC_r(p,r)$ are divisible by $p$? By divisible I mean $_nC_r(p,r)/p$ leaves remainder $0$.

oivind

  • 1
    Look for [Lucas's theorem](http://en.wikipedia.org/wiki/Lucas%27_theorem)2012-05-25

2 Answers 2