1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Discrete Math Question

  1. Nov 12, 2014 #1
    Prove the following theorem:
    Theorem For a prime number p and integer i,
    if 0 < i < p then p!/[(p− i)! * i] * 1/p

    Not sure how to go about this. I wanted to do a direct proof and this is what Ive got so far.
    let i = p-n
    then p!/[(p-n)!*(p-n)] but that doesnt exactly prove much.
     
  2. jcsd
  3. Nov 12, 2014 #2

    RUber

    User Avatar
    Homework Helper

    hlzombi,
    First, please note that you should use the template and this seems like it might be better to place in the math forum.
    ##\frac{p!}{(p-n)!*(p-n)}=\frac{p*(p-1)*...*(p-n+1)}{p-n}##
    Finally, I am not sure what you are asked to prove...is there some equality or property here?
    You need to be more clear.
     
  4. Nov 12, 2014 #3
    Apologies, I'm new here. I tried to follow the template as best as I could.

    To clarify, I'm trying to prove the theorem p!/[(p− i)! * i] * 1/p where 0<i<p when p is a prime number and i is an integer.
     
  5. Nov 12, 2014 #4

    pasmith

    User Avatar
    Homework Helper

    Your statement is incomplete. What are you trying to prove about [itex]\frac{p!}{(p-i)!i} \times \frac 1p[/itex] when [itex]p[/itex] is prime and [itex]i[/itex] is an integer?
     
  6. Nov 12, 2014 #5
    Im trying to verify the theorem under those conditions
     
  7. Nov 12, 2014 #6

    RUber

    User Avatar
    Homework Helper

    You did not write the theorem.
     
  8. Nov 12, 2014 #7
  9. Nov 12, 2014 #8

    RUber

    User Avatar
    Homework Helper

    That says p divides p choose i. That is not what you wrote above.
     
  10. Nov 12, 2014 #9

    RUber

    User Avatar
    Homework Helper

    To demonstrate this, you can use induction.
    Show that for a base case (i=1) ##p\left| \left( \begin{array}{c} p\\i\end{array}\right) \right. ##
    Assume for some n < p-1, the statement holds.
    Show that ##p\left| \left( \begin{array}{c} p\\n+1 \end{array}\right) \right. ##
     
  11. Nov 12, 2014 #10

    Mark44

    Staff: Mentor

    When you use the template, don't delete its three parts.

    Also, I moved this thread, as it was better suited in one of the math sections.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Discrete Math Question
  1. Discrete Math Question (Replies: 1)

  2. Discrete Math Question (Replies: 2)

Loading...