Transcendental solutions of Fermat-type functional equations in Cn

The equation f(n) + g(n) = 1 can be interpreted as the Fermat Diophantine equation x(n) + y(n )= 1 within the function field when n is a positive integer. This study employs Nevanlinna theory for several complex variables to explore transcendental solutions of Fermat-type functional equations with polynomial coefficients in Cn. If the coefficients of the equation are transcendental functions and satisfy a certain relationship, we show that transcendental solutions can be obtained. Moreover, we determine the precise form of the solutions in both cases.