ON GENERALIZED FERMAT DIOPHANTINE FUNCTIONAL EQUATIONS IN Cn AND PICARD TYPE THEOREMS

This paper concerns entire and meromorphic solutions of the generalized Fermat Diophantine functional equations hf(p) + kg(q) = 1 in C-n, where h, k are meromorphic coefficients in several complex variables and p, q >= 1 are integers with (p, q) not equal (1, 1). As applications, we determine when entire solutions of the simple-looking functional equation f(p) + g(q) = 1 in C reduce to constant and then apply the result to show two well-known Picard type theorems in a direct manner.