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Thread: Todays Quiz Question

  1. #1 Todays Quiz Question 
    Forum Professor river_rat's Avatar
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    Show that for any prime , the number is divisible by 24.

    PS. If you get it don't post your answer right away.[/tex]


    As is often the case with technical subjects we are presented with an unfortunate choice: an explanation that is accurate but incomprehensible, or comprehensible but wrong.
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  3. #2  
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    Not true for p= 2 or 3.


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  4. #3  
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    Divisible to produce an integer or any real number?
    I had a simple dream: a dream to kill all humans, and this is how you repay me?
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  5. #4 Re: Todays Quiz Question 
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    Quote Originally Posted by river_rat
    Show that for any prime > 3, the number is divisible by 24.

    PS. If you get it don't post your answer right away.[/tex]
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  6. #5  
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    huh, i guess it does work.

    cant prove it though, at least i cant be bothered to.
    I had a simple dream: a dream to kill all humans, and this is how you repay me?
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  7. #6  
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    If , then so either or is divisible by 3. Also or are consecutive even integers, so their product is divisible by 8. Hence is divisible by .

    Sorry, river_rat, can’t help posting my solution right away. I did PM my solution to you at first, but in view of the post above, I simply have to teach some lazy bugger here a lesson on how maths should be done.

    To make up for it, I can post the next quiz question when everyone’s ready.
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  8. #7  
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    yeah well screw you too
    I had a simple dream: a dream to kill all humans, and this is how you repay me?
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  9. #8  
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    Mod note

    Jane, Jek, please keep it civil, there's nothing to gained by name-calling and the like.

    Thank you

    -G-
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  10. #9  
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    haha im reading the question and im thinking to myself that theres no way the first couple of primes makes sense unless you are not talking about whole numbers.
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  11. #10  
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    Next quiz question.

    If is an integer not divisible by 5, prove that is divisible by 20.

    [Note to dumb ass: 0 is divisible by all integers!]
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  12. #11  
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    Try n =0 or 1 or 2 smart ass!
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  13. #12  
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    See note to dumb ass above.
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  14. #13  
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    Mod note Jane, please try to remain civil. Nothing is gained by name-calling
    -G-
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  15. #14  
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    Proof:



    Since , we have 5 consecutive numbers {n-2, n-1, n, n+1, n+2} such that the middle one isn't divisible by 5, so one of the others must be. Therefore, .

    Similarly, if , then one of {n-2, n-1, n+1} is divisible by 4. If , then . Either way, .

    Since 4 and 5 are relatively prime, .
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  16. #15  
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    Very nicely done, MagiMaster!



    By the way, when mathematicians write , they usually mean divides , not is divisible by . But I understand what you mean.
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  17. #16  
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    Quote Originally Posted by JaneBennet
    is divisible by 5. I did say that should not be divisible by 5. Are you blind, or just a moron?

    And what is wrong with or ?
    Lol, No but at 73 I'm fast heading towards both, something i'm sure your attititude will not let you live long enough to see!
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  18. #17  
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    Quote Originally Posted by JaneBennet
    Very nicely done, MagiMaster!



    By the way, when mathematicians write , they usually mean divides , not is divisible by . But I understand what you mean.
    Jane i absolutely love your avatar... it's almost.... theraputic.
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  19. #18  
    Forum Radioactive Isotope MagiMaster's Avatar
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    @Jane, Oh. It's been a while since I've used that symbol, so I think I just wrote it backwards. :P

    @Megabrain, I think you made the mistake of assuming 0 is not divisible by anything, when it's actually divisible by everything. (Another way of saying that is that any integer can be multiplied by something to get 0.)
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  20. #19  
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    Mod note I have split this thread, as requested. I offer abject apologies for mis-spelling in the new title - I cannot figure how to edit it,
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  21. #20  
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    Let be an integer not divisible by 7. Prove that is divisible by 56.
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