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if integers x and y satisfy 2008x=16y , the smallest possible value of x+y is______.

  • algebra -

    Using positive integers,
    since 2008=8*251 and 16 = 8*2,
    251x = 2y

    x=2, y=251 gives x+y=253

    If you allow zero, then 0+0=0 is the minimum.

    now, if you allow negative integers, then there is no minimum value.

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