The entire solution pairs of a class of Fermat-type difference equation systems on $ \mathbb{C}^2 $

Zhuo Wang; Qingcai Zhang; Zhuo Wang; Qingcai Zhang

doi:10.3934/math.20251226

AIMS Mathematics

2025, Volume 10, Issue 11: 27921-27933. doi: 10.3934/math.20251226

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Research article

The entire solution pairs of a class of Fermat-type difference equation systems on $ \mathbb{C}^2 $

Zhuo Wang ¹,
Qingcai Zhang ^{2
,
,}

1.
College of Information Science and Technology, Gansu Agricultural University, Lanzhou 730070, China
2.
School of Mathematics, Renmin University of China, Beijing 100872, China

Received: 27 July 2025 Revised: 24 October 2025 Accepted: 05 November 2025 Published: 28 November 2025
MSC : 32A08, 32A15, 32A22

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 $ \mathbb{C}^2 $ and have derived results that are distinct from those in the single complex variable case.
- Nevanlinna theory,
- two-variable polynomials,
- finite-order entire solutions,
- Fermat-type functional equations on $ \mathbb{C}^2 $
Citation: Zhuo Wang, Qingcai Zhang. The entire solution pairs of a class of Fermat-type difference equation systems on $ \mathbb{C}^2 $[J]. AIMS Mathematics, 2025, 10(11): 27921-27933. doi: 10.3934/math.20251226

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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 $ \mathbb{C}^2 $ and have derived results that are distinct from those in the single complex variable case.

References

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