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  1. 11th March 2008, 01:59 PM #16
    Frank&Earnest
    Frank&Earnest is offline GOLD MEMBER
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    Quote Originally Posted by Greg Ward View Post
    6 is the answer, for the gardener planted seeds (plural).

    Any cubed number divided by 7 has only 3 remainders (not reminders Wongo, but I shared your excitement yesterday): 0, 1 or 6

    1 cubed: 1/7. remainder; 1
    2 cubed: 8 /7 remainder: 1
    3 cubed: 27/7 remainder: 6
    4 cubed: 64/7. remainder: 1
    5 cubed: 125/7 remainder: 6
    6 cubed: 216/7 remainder: 6
    7 cubed: 343/7 remainder: 0

    Can anyone prove that these are the only 3 solutions for all cubed numbers divided by 7?


    Greg
    The Butcher got his cuts mixed up, but basically already gave you the answer: the problem is a cubic function that has three real roots (you can check on wikipedia, this time they got it right).
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  3. 12th March 2008, 01:47 PM #17
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    Wongo
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    Quote Originally Posted by Greg Ward View Post
    Any cubed number divided by 7 has only 3 remainders (not reminders Wongo, but I shared your excitement yesterday): 0, 1 or 6

    1 cubed: 1/7. remainder; 1
    2 cubed: 8 /7 remainder: 1
    3 cubed: 27/7 remainder: 6
    4 cubed: 64/7. remainder: 1
    5 cubed: 125/7 remainder: 6
    6 cubed: 216/7 remainder: 6
    7 cubed: 343/7 remainder: 0

    Can anyone prove that these are the only 3 solutions for all cubed numbers divided by 7?
    14 cubed: 2744 / 7 remainder: 0
    21 cubed: 9261 / 7 remainder: 0
    28 cubed: 21952 / 7 remainder: 0
    35 cubed: 42875 / 7 remainder: 0

    I found 4.
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  4. 12th March 2008, 04:19 PM #18
    Frank&Earnest
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    Quote Originally Posted by Wongo View Post
    14 cubed: 2744 / 7 remainder: 0
    21 cubed: 9261 / 7 remainder: 0
    28 cubed: 21952 / 7 remainder: 0
    35 cubed: 42875 / 7 remainder: 0

    I found 4.
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  5. 12th March 2008, 04:27 PM #19
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    Wongo
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    Can anyone prove that these are the only 3 solutions for all cubed numbers divided by 7?

    NOT

    Can anyone prove that there are the only 3 solutions for all cubed numbers divided by 7?


    Sorry I read the question incorrectly. I knew it was something wrong with it.

    See I am not perfect after all.

    Such good reputation huh.

    My bad.
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