Meromorphic solutions of Fermat type partial differential equations

Abstract The main purpose of this paper is to describe the pseudo-primeness of the meromorphic solutions of the Fermat type functional equation F ( u z 1 , ⋯ , u z n ) + u k = 1 , where F ( z 1 , ⋯ , z n ) is a nonconstant homogeneous polynomial with degree m in n variables z 1 , ⋯ , z n and k is a positive integer. In addition, we give a simple proof and strengthening of a theorem which is related to the Fermat type functional equation f 3 + g 3 = 1 in C 2 by improving the condition so that f z 2 and g z 1 have the same zeros (ignoring multiplicities).