# algebra

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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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