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All meromorphic solutions of Fermat-type functional equations (2404.10248v2)

Published 16 Apr 2024 in math.CV

Abstract: In this paper, by making use of properties of elliptic functions, we describe meromorphic solutions of Fermat-type functional equations $f(z){n}+f(L(z)){m}=1$ over the complex plane $\mathbb{C}$, where $L(z)$ is a nonconstant entire function, $m$ and $n$ are two positive integers. As applications, we also consider meromorphic solutions of Fermat-type difference and $q$-difference equations.

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