Translate an English sentence having exactly/only one condition in First Order Logic

Question

Our job is to translate the following sentence to first order logic:

"The public university in Melbourne was built on the land of the Torres Strait Islander peoples."

We can only use one variable: u which represents all universities.
We can only use the following two predicates: Public(u), and TorresLand(u) and u represents a university.

How do I go about translating this sentence? From what I understand, I can translate like this:
$∃u$ [Public($u$) $∧$ TorresLand($u$)]

But it look like that "The public university" implies only one public university is present at the given location. How do I translate the requirement of exactly/only one into First Order Logic?

EDIT: Based on one of the answers provided below, I am providing another predicate Melbourne(u) to preserve info about the location of the public university. Based on this new info, is my answer below correct:
∃u [(Public(u) ∧ Melbourne(u) ∧ ∀v(Public(v) ∧ Melbourne(v) → v = u) ∧ TorresLand(u)]

Answer 1

But it look like that "The public university" implies only one public university is present at the given location. How do I translate the requirement of exactly/only one into First Order Logic?

What you are asking for is referred to as uniqueness quantification $\exists!$ (i.e., there exists exactly one X), as opposed to existential quantification $\exists$ (i.e., there exists one or more X).

We can quite straightforwardly formulate, as follows, the uniqueness quantifier $\exists!$ in terms of an ordinary existential quantifier $\exists$ along with an existential quantifier $\exists$ (or universal quantifier $\forall$)

$$\underbrace{\exists! xP(x)}_{\text{There is exactly one $x$ that satisfies $P$}}\iff \underbrace{\exists x}_{\text{There is an $x$}}\,( \underbrace{P(x)}_{\text{for which $P$ holds}} \, \wedge \underbrace{\neg \exists y\,(P(y) \wedge y \ne x)}_{\text{and no $y$ other than $x$ satisfies $P$}})$$

So you could translate that the indicated $u$ is the one and only public university as

$$\exists u\,\left(\operatorname{Public}(u)\wedge \neg \exists y \left(\operatorname{Public}(y)\wedge y\neq u\right)\right)$$

But as to whether or not that is what your teacher is looking for, I have no idea. We are already necessarily losing (as a predicate at least) the information that the university is in Melbourne, so it may not be important that we lose the information of the uniqueness of $u$.