As far as I know, whether Fermat's Last Theorem is provable in Peano Arithmetic is an open problem. What is known about this problem?

In particular, what is known about the arithmetic systems $PA + \text{Fermat's Last Theorem}$ and $PA + \lnot \text{Fermat's Last Theorem}$?

Note in particular that if $PA \vdash \text{Fermat's Last Theorem}$, the first system will just be $PA$ and the second system with be inconsistent. If FLT is independent of PA, then both will be consistient systems distinct from PA. $PA \vdash \lnot \text{Fermat's Last Theorem}$ is not possible, since $PA$ and Fermat's last theorem are both true in $\mathbb N$.

As far as I know, whether Fermat's Last Theorem is provable in Peano Arithmetic is an open problem. What is known about this problem?

In particular, what is known about the arithmetic systems $PA + \text{Fermat's Last Theorem}$ and $PA + \lnot \text{Fermat's Last Theorem}$?

Note in particular that if $PA \vdash \text{Fermat's Last Theorem}$, the first system will just be $PA$ and the second system with be inconsistent. If FLT is independent of PA, then both will be consistient systems distinct from $PA$. $PA \vdash \lnot \text{Fermat's Last Theorem}$ is not possible, since $PA$ and Fermat's last theorem are both true in $\mathbb N$.