Existence of meromorphic solutions of some generalized Fermat functional equations.

The aim of this paper is twofold. Firstly, we study the non-existence of finite order meromorphic solutions to the Cubic type of Fermat functional equation f (z) 3 - 3 τ f (z) f (z + c) + f (z + c) 3 = 1 . In addition, the paper is concerned with the description of finite order entire solutions of the Quadratic type of Fermat functional equation f (z) 2 - 2 μ f (z) f (z + c) + f (z + c) 2 = 1 . [ABSTRACT FROM AUTHOR]