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8n divides (4n)! Proof by induction

  1. Dec 7, 2008 #1
    1. The problem statement, all variables and given/known data
    I need to do this by proof by induction
    8n divides (4n)!

    2. Relevant equations



    3. The attempt at a solution
    I already did it for 1, now I need to do for k and k+1
    (4k)!t=8k
     
  2. jcsd
  3. Dec 7, 2008 #2
    If 8k divides (4k)!, how can 8k be a multiple of (4k)! as you wrote?
     
  4. Dec 7, 2008 #3
    [tex]8^{k}[/tex] divides (4k)!
    [tex]8^{k}[/tex]*t=(4k)!
     
  5. Dec 7, 2008 #4
    Simplify (4(k + 1))! in terms of (4k)!
     
  6. Dec 7, 2008 #5
    (4k+4)!=(4k+4)(4k+3)(4k+2)(4k+1)(4k)!
     
  7. Dec 7, 2008 #6
    You already know that [tex]8^k[/tex] divides (4k)!, so does 8 divide everything else?
     
  8. Dec 7, 2008 #7
    Yes....
     
  9. Dec 7, 2008 #8
    Then you have all the details for the complete proof.
     
  10. Dec 7, 2008 #9
    Ok, I see....
     
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