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Research Article | Open Access

The entire solution pairs of a class of Fermat-type difference equation systems on C 2

Zhuo Wang1, Qingcai Zhang2( )
College of Information Science and Technology, Gansu Agricultural University, Lanzhou 730070, China
School of Mathematics, Renmin University of China, Beijing 100872, China
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Abstract

For two-variable polynomials, we have identified periodicity characteristics that differ from those of the single-variable polynomials. In this paper, based on the research of [1], we have further investigated the finite-order entire solution pairs for the generalized quadratic trinomial Fermat-type functional equation systems on C 2 and have derived results that are distinct from those in the single complex variable case.

Keywords

Nevanlinna theorytwo-variable polynomialsfinite-order entire solutionsFermat-type functional equations on C2
CLC number: 32A08, 32A15, 32A22

References

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AIMS Mathematics
Volume 10 Issue 11,
November 2025
Pages 27921-27933
DOI: 10.3934/math.20251226

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Cite this article:
Wang Z, Zhang Q. The entire solution pairs of a class of Fermat-type difference equation systems on C 2 . AIMS Mathematics, 2025, 10(11): 27921-27933. https://doi.org/10.3934/math.20251226

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Received: 27 July 2025
Revised: 24 October 2025
Accepted: 05 November 2025
Published: 28 November 2025
©2025 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)