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Register a new userOn generalized Fermat Diophantine functional and partial differential equations in $mathbf{C}^2$
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In this paper, we characterize meromorphic solutions $f(z_1,z_2),g(z_1,z_2)$ to the generalized Fermat Diophantine functional equations $h(z_1,z_2)f^m+k(z_1,z_2)g^n=1$ in $mathbf{C}^2$ for integers $m,ngeq2$ and nonzero meromorphic functions $h(z_1,z_2),k(z_1,z_2)$ in $mathbf{C}^2$. Meromorphic solutions to associated partial differential equations are also studied.
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