On Entire solutions of system of Fermat-type difference and partial differential-difference equations in ℂⁿ

2023/10/31 by Goutam Haldar, Haldar, Goutam
Mathematics · #30D35 #32H30 #35A20 #39A14 #39A45 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry and Number Theory #Complex Variables (math.CV) #FOS: Mathematics #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.2310.20358

openalex publication_date 2023/10/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The equation fⁿ+gⁿ=1, n∈ℕ can be regarded as the Fermat Diophantine equation over the function field. In this paper we study the characterization of entire solutions of some system of Fermat type functional equations by taking e^g₁(z) and e^g₂(z) in the right hand side of each equation, where g₁(z) and g₂(z) are polynomials in ℂⁿ. Our results extend and generalize some recent results. Moreover, some examples have been exhibited to show that our results are precise to some extent.

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