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What is the sum of all integer values of n such that 3n+15/(n−1)(n−5) is also an integer

  • maths -

    since (n-1)(n-5) <= 3n+15 for -1 <= n <= 10, that limits our choices

    listing the values of n, (3n+15) and (n-1)(n-5), we have

    -1 12 14 no
    0 15 5 YES
    1 18 0 no
    2 21 -3 YES
    3 24 -4 YES
    4 27 -3 YES
    5 30 0 no
    6 33 5 no
    7 36 12 YES
    8 39 21 no
    9 42 32 no
    10 45 45 YES

    0+2+3+4+7+10 = 26

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