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Math Help - Tracing numbers - Induction needed ?

  1. #1
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    Unhappy Tracing numbers - Induction needed ?

    Hi !

    is it true that any set of tracing numbers (1, 2, 3, 4...) can be divided (no remainder) by the factorial n!, whereas "n" is the numbers of integers in the group ?

    example: 3, 4, 5, 6 (n = 4)
    can be devided by: 4! = 24.

    and how can i prove it...?

    thanx a lot !
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  2. #2
    hpe
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    Quote Originally Posted by dudinka
    Hi !

    is it true that any set of tracing numbers (1, 2, 3, 4...) can be divided (no remainder) by the factorial n!, whereas "n" is the numbers of integers in the group ?

    example: 3, 4, 5, 6 (n = 4)
    can be devided by: 4! = 24.

    and how can i prove it...?

    thanx a lot !
    If I understand you correctly you want to prove that (k-n+1) \cdot (k-n+2) \cdot \dots \cdot k (n factors, starting at k-n+1)is always divisible by  n!, regardless what k and n are.
    This is correct, the quotient is \binom{k}{n} which is always an integer.
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  3. #3
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    thank you

    thanks a lot.
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