1, 2 and 3.
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The first three positive integers, 1, 2, and 3, satisfy this condition.
The set of integers is divided into three subsets. One is the positive integers. Another is the negative integers. The last subset has one element -- zero. In sum, integers are composed of the positive integers, the negative integers, and zero.
The 3 consecutive odd positive integers are 7, 9 and 11.
The sum of the first three even positive integers is 2 + 4 + 6 = 12.
It may be either. If any of the integers is zero, the product will be zero. Else, if one or three of the integers is negative, the product will be negative. Otherwise, it will be positive.