Question
The sum of three different integers can never be zero.

Answer

False.
e.g. Let the three integers be $2, 3$ and $-5.$
Sum of $2,3$ and $-5 = 2 + 3 + (-5)$
$= 2 + 3 - 5$
$= 5 - 5 = 0$
Clearly, the sum of three different integers can be zero.

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