Fermat’s equation for matrices or quaternions over \(q\)-adic fields. (English) Zbl 1053.11026
Let \(n\) be a positive integer with \(n> 1\). In this paper the author considers the existence of solutions \((X,Y,Z)\) of the equation \(X^n+ Y^n= Z^n\) which are square matrices or quaternions over the field \(\mathbb{Q}_p\) of \(p\)-adic numbers.
Reviewer: Le Maohua (Zhanjiang)
MSC:
11D41 | Higher degree equations; Fermat’s equation |
11D88 | \(p\)-adic and power series fields |
11S45 | Algebras and orders, and their zeta functions |