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Just to verify

  1. May 5, 2009 #1
    [tex]
    \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)?
     
  2. jcsd
  3. May 5, 2009 #2

    Dick

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    Are these like two totally separate problems? I don't know what the second has to do with the first. The first one is just a 'find the common denominator' problem and show both sides are equal. Use C(n,k)=n!/(k!*(n-k)!).
     
  4. May 6, 2009 #3
    [tex]
    \frac{n!}{(n-k)!k!}+\frac{n!}{(n-k)!(k+1)!}
    [/tex]
    [tex]
    \frac{n!}{(n-k-1)!(k+1)}+\frac{n!}{(n-k)!(k+1)!}
    [/tex]
    [tex]
    \frac{(n+1)!}{(n-k)!(k+1)!}
    [/tex]
    [tex]
    \binom{n+1}{k+1}
    [/tex]
     
  5. May 6, 2009 #4

    Dick

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    The first line isn't even correct. C(n,k+1)=n!/((k+1)!*(n-k-1)!).
     
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