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Math Help - Need to find four-figure number.

  1. #1
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    Exclamation Need to find four-figure number.

    Hello

    I need to find a four-figure number which can be divided by 7 and which can be written as a sum of square and cube of any natural number..
    My English is not perfect, but I hope you will understand what I mean.

    I would be very glad if someone could help me.
    Last edited by Sott; February 19th 2013 at 04:36 AM.
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  2. #2
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    Re: Need to find four-figure number.

    H. Please write me personal in skype: agripasiga i'wiill try to help solve you problem
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  3. #3
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    Re: Need to find four-figure number.

    You can write here.
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  4. #4
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    Re: Need to find four-figure number.

    10^3 + 1^2 = 1001 which is divisable by 7 143 times.
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    Re: Need to find four-figure number.

    By the way: the square and the cube has to be of the same natural number. For example 10^2 + 10^3
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  6. #6
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    Re: Need to find four-figure number.

    It looks to me like this is just a matter of trying! We are looking a number, x, such that x^2+ x^3 has four digits and is divisible by 7. Since 7 is prime, that means that x must be divisible by 7. 7^3= 343 so for x^3 to be four digits itself the other factor in x^3 must be between 3 and 30. The only cubes in that interval are 1= 1^3, 8= 2^3, and 27= 3^3 so the only possible values for x are 7(1)= 7, 7(2)= 14, and 7(3)= 21.

    If x= 7, then 7^2+ 7^3= 49+ 343= 392 which does not have four digits. If x= 14, then 14^2+ 14^3= 196+ 2744=2940= 7(420). That has four digits and so is a perfectly good answer. If x= 21, then 21^2+ 21^3= 441+ 9261= 9702= 7(1386). Both 2940 and 9702 fit the requirements.
    Last edited by HallsofIvy; February 19th 2013 at 08:03 AM.
    Thanks from Sott
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  7. #7
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    Re: Need to find four-figure number.

    Ok then, 14^3 + 14 ^ 2 which divided by 7 is 420.. May I have a thanks?
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  8. #8
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    Re: Need to find four-figure number.

    HallsofIvy Interesting explanation. My answer was 13, because 13^2+13^3 is 2366 and 2366 : 7 = 338, but I had no idea how to explain that. I think your solution is enough good. I don't know how to find the answer in other ways.
    Last edited by Sott; February 19th 2013 at 05:32 AM.
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