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Divisibility math problem

  1. Oct 13, 2010 #1
    1. The problem statement, all variables and given/known data

    i want to show if n = pq, 1 < p < n, then p l (n-1)!

    2. Relevant equations

    n/a

    3. The attempt at a solution

    i can see its true, because p < n, p l p, then p l (n-1)!. and this prove very ambiguous for me

    2 question.

    1.help me, i think there must be easier way to prove the question

    2. btw, how do i prove those bold statement?

    if 1 < p < n, p l p, then p l (n-1)! its something like this p l (1)....(p)....(n-1)!, help T_T
     
  2. jcsd
  3. Oct 13, 2010 #2

    Mark44

    Staff: Mentor

    Re: divisibility

    Here's an example (not a proof!) to show what's going on.

    Let n = 21 = 7 * 3, with p = 7 and q = 3.

    Does p | 20! ? Since 20! = 1 * 2 * 3 * ... * 6 * 7 * 8 * ... * 19 * 20, p clearly divides (n - 1)! in this example.
     
  4. Oct 13, 2010 #3
    Re: divisibility

    i know, that's what i already see. but how should i prove it T_T,
     
  5. Oct 13, 2010 #4

    Mark44

    Staff: Mentor

    Re: divisibility

    Show that, since p < n, then there is a factor of p in (n - 1)!. A proof by induction is one way to go. There might be a simpler way, but it doesn't occur to me.
     
  6. Oct 13, 2010 #5
    Re: divisibility

    i'll try by induction, thank you ^^
     
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