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Math Help - Arithmetic problem

  1. #1
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    Arithmetic problem

    What is the largest positive integer n for which there is a unique integer k such that

    8/15 < n/(n+K) < 7/13

    please help
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  2. #2
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    this could be helpful

     \frac{8}{15} < \frac{n}{n+K} < \frac{7}{13}

     \frac{104}{195} < \frac{n}{n+K} < \frac{105}{195}

     104 < \frac{195n}{n+K} < 105
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  3. #3
    Super Member Bacterius's Avatar
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    \frac{8}{15} < \frac{n}{n+K} < \frac{7}{13}

    Multiply by a common divisor of 15 and 13 so as to get everything in integers.

    \frac{104}{195} < \frac{195n}{195(n+K)} < \frac{105}{195}

    Multiply everything by 195 so we get integers ...

    104 < \frac{195n}{n+K} < 105

    It might help ...

    EDIT : oh, no ! owned by Pickslides ! (nearly the same contents though)
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