Abstract
In this paper, we study Fermat-type functional equations \(f^n+g^n+h^n=1\) in the complex plane. Alternative proofs of the known results for entire and meromorphic solutions of such equations are given. Moreover, some conditions on degrees of polynomial solutions are given.
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Acknowledgements
The authors would like to thank Professor Gary G. Gundersen for his valuable suggestions. The authors would also like to thank the referees for their helpful comments. This research has financially been supported by the discretionary budget (2017) of the President of the Open University of Japan.
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Communicated by Ilpo Laine.
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Ishizaki, K., Kimura, N. Entire and Meromorphic Solutions of the Functional Equation \(f^n+g^n+h^n=1\) and Differential Equations. Comput. Methods Funct. Theory 19, 157–172 (2019). https://doi.org/10.1007/s40315-018-0258-y
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DOI: https://doi.org/10.1007/s40315-018-0258-y
Keywords
- Fermat-type functional equations
- Polynomials
- Rational functions
- Meromorphic functions
- Entire functions
- Nevanlinna theory