Entire and Meromorphic Solutions of the Functional Equation f~n + g~n + h~n = 1 and Differential Equations

摘要

In this paper, we study Fermat-type functional equations fn+gn+hn=1 in the complex plane. Alternative proofs of the known results for entire and meromorphic solutions of such equations are given. Moreover, some conditions on degrees of polynomial solutions are given.