Generalize the statement of FermatLastTheorem to accommodate different kinds of rings (e.g. $R = k[X]$) and trivial solutions. A relevant Zulip discussion here.

Fermat's Last Theorem states the following for ring $R = \mathbb{Z}$ (or semiring $R = \mathbb{N}$).

Statement 1 ('zero' version): For any solutions to $a^n + b^n = c^n$ we have $abc=0$.

The Mason--Stothers theorem gives a polynomial variant of FLT for ring $R = k[X]$ with $k$ characteristic zero. But we have to change the notion of trivial solutions.

Statement 2 ('unit' version): For any solutions to $a^n + b^n = c^n$, the triple $(a, b, c)$ is a common multiple of $(a', b', c')$ where each $a', b', c'$ is either zero or unit.

We note the followings.

1. For $R = \mathbb{N}, \mathbb{Z}$ the statements 1 and 2 are equivalent.
2. However, for $R = \mathbb{Q}$ statement 1 is equivalent to full FLT but statement 2 is trivial.
3. The equivalence of statements 1 and 2 for $R = \mathbb{N}, \mathbb{Z}$ also requires a bit of juggling with definitions albeit trivial.
4. For $R = k[X]$, statement 1 is likely false but statement 2 is true.
5. In "Fermat's Last Theorem over Number Fields" by N. Freitas, the author mostly mentions statement 1 as a generalization, but also mentions many 'trivial' solutions outside statement 1.

The relationship between statements 1 and 2 in general:

1. If $R$ is a Dedekind domain (e.g. integral ring) then it seems that zero version implies the unit version.
2. If the sum of two units in $R$ is never a unit in $R$, then the unit version implies the zero version. Here it is mentioned that the integral ring of $\mathbb{Q}(\sqrt{d})$ for $d < 0$ satisfy the condition unless $d = 2, 3, 6$.

This PR attempts to capture such minor differences in the notion of 'trivial' solutions.

1. We provide a general statement for stating FLT with arbitrary notion of 'trivial' solutions. Then we give Statements 1 and 2 as specific instances.
2. Since we are much more familiar with 'zero' version (Statement 1), we define the main FLT for integers with Statement 1.
3. We show the equivalence between Statements 1 and 2 for $R = \mathbb{N}, \mathbb{Z}$
4. We state the polynomial FLT with statement 2. This will be proved when we port the project I did with @seewoo5 here.