Characterizations of entire solutions for the system of Fermat-type binomial and trinomial shift equations in ℂn

In this article, we investigate the existence and the precise form of finite-order transcendental entire solutions of some system of Fermat-type quadratic binomial and trinomial shift equations in . Our results are the generalizations of the results of [H. Y. Xu, S. Y. Liu, and Q. P. Li, , J. Math. Anal. Appl. (2020), 123641, 1–22, DOI: ] and [H. Y. Xu and Y. Y. Jiang, , RACSAM (2022), 8, DOI: .] to a large extent. Most interestingly, as a consequence of our main result, we have shown that the system of quadratic trinomial shift equation has no solution when it reduces to a system of quadratic trinomial difference equation. In addition, some examples relevant to the content of the article have been exhibited.