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Math Help - Please help

  1. #1
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    Question Please help

    Please help:

    Find all composite integers M such that the product 2005 * M has exactly eight divisors.
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  2. #2
    hpe
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    Quote Originally Posted by mathsmad
    Please help:

    Find all composite integers M such that the product 2005 * M has exactly eight divisors.
    M = 2005 = 5*401, M = 25, M = 401*401 all work.

    If M is allowed to be prime, any prime number not equal to 5 or 401 will do.
    If M is composite and has a prime factor other than 5 or 401, there will be too many factors. Similar if M is divisible by 5*5*401 or 5*401*401.

    So only powers of 5 or 401 remain. Counting divisors for the cases M = 5^k, k > 2 and M = 401^k, k > 2 shows that these have too many divisors. This implies that the cases given above are the solution set.
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  3. #3
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    Cool Thanks for the help

    Thanks for the help
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