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\binom{n+1}{k+1}=\binom{n}{k}+\binom{n}{k+1}

[/tex]

I'm not sure how to prove this.

However...does this work:

If p is a positive prime number and 0<k<p, prove p divides [tex]\binom{p}{k}[/tex]

Can't I just say that if that binomial is prime, this means that it is only divisible by p and 1 (since we are only working in the positive)?