Question

The notation ∃!xP(x) denotes the proposition "There exists a unique x such that P(x) is true."
If the universe of discourse is the set of integers, what are the truth values of the following?
1. ∃!x(x>1)
2. ∃!x(x2=1)
3. ∃!x(x+3=2x)
4. ∃!x(x=x+1)

What I got was:
1. F
2. T
3. T
4. F
but one of them isn't correct and I'd like to understand why