On The Meromorphic Solutions Of Fermat - Type Diophantine Function Equation

This thesis studies the meromorphic functional solutions of Fermat type functional equation and proves the following results by the value distribution theory of meromorphic function and normal families theory·For n>3, we give a new proof of the result there do not exist two nonconstant entire functions f(z) and g(z) that satisfy f~n(z)+g~n(z)=1.·Let f(z), g(z), h(z) be meromorphic functions in the plane of order ρ_f<1/2.If f(z), g(z), h(z) have at most one common simple pole, then there do not exist three nonconstant meromorphic functions f(z), g(z), and h(z) that satisfy f~7(z)+g~7(z)+h~7(z)=1.·For n≥13, there do not exist three nonconstant meromorphic functions f(z), g(z), and h(z) that satisfy f~n(z)+g~6(z)+h~6(z)= z.