Can sombebody help me with the following question?
I'm trying to study the Fermat´s equation $X^{n}+Y^{n}=Z^{n}$ over some non-conmutative rings such as $M_{n\times n}(\mathbb{Z})$. Are there solutions? What are all the solutions? On the other hand: it would be interesting study that equation over the ring $\mathbb{H}$ of Hamilton's quaternions?
I want to write my first paper on some Diophantine equations on different rings, specially different from $\mathbb{Z}$