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Find the smallest positive integer N that satisfies all of the following conditions:

• N is a square.

• N is a cube.

• N is an odd number.

• N is divisible by twelve prime numbers.

How many digits does this number N have?

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11 answers

  1. Hey 👋

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  2. to be odd, it cannot have 2 as a factor.

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  3. Of course, good checkup oobleck.

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  4. are you sure, you answerd all the points of it.

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  5. Please anser my question. Urgent!

    If any one can solve; please do and share the answer in step by step.

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  6. obviously we have to take out the factor of 2 since multiplying anything
    by 2 would make it even, so

    3*5*7*11*13*17*19*23*29*31*37

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  7. Please answer the question in detail.

    In step by step.

    Answer full, not hints.

    Please Answer ASAP.

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  8. I understand your approach; thanks

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  9. Please answer the question in detail.

    In step by step.

    Answer full, not hints.

    Please Answer ASAP

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  10. 12/3/2008
    Birth of date

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  11. The trouble is the divisibility by the first 12 prime numbers,
    so it must be a multiple of 2*3*5*7*11*13*17*19*23*29*31*37

    To be odd it must look like 2K+1

    to be a square it must look like (2K+1)^2, and it must also be a cube
    it must contain (2K+1)^6

    so, it must have the form:
    2*3*5*7*11*13*17*19*23*29*31*37(2K+1)^6
    when K = 0, we get
    2*3*5*7*11*13*17*19*23*29*31*37(1)^6
    = 7.420738135... x 10^12
    which would be 13 digits long

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