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Math Help - Divisibility by 30

  1. #1
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    Divisibility by 30

    Does any one want to try this. I spent hours on it.

    prove that 30| n^9 - n.
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  2. #2
    Super Member TheChaz's Avatar
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    I might take a crack at it, but don't want to duplicate your work. What have you tried?

    Do you know how to use the Principle of Mathmatical Induction?
    Can you state divisibility by 30 in any other way?
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  3. #3
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    Quote Originally Posted by karlito03 View Post
    Does any one want to try this. I spent hours on it.

    prove that 30| n^9 - n.

    Without induction:

    n^9-n=n(n^8-1)=n(n^4-1)(n^4+1)=n(n^2-1)(n^2+1)(n^4+1)=n(n-1)(n+1)(n^2+1)(n^4+1).

    Well, now just prove that the above is always divisible by 2, by 3 and by 5 and you're done.

    Tonio
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  4. #4
    Super Member TheChaz's Avatar
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    How about "without spoon-feeding"?
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  5. #5
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    Quote Originally Posted by TheChaz View Post
    How about "without spoon-feeding"?
    Thank you Tonio, I thought of it this way, but I kept getting stocked at some point.
    "TheChaz" try ur induction as you suggested it and then you tell me how u will feel!.
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  6. #6
    Super Member TheChaz's Avatar
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    My reply wasn't a defense of induction for this problem (which you have apparently seen as inefficient!); it was a criticism of (possibly) keeping you from the problem solving process.
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