A holomorphic mapping \(f: {\mathbb {C}} \rightarrow {\mathbb {P}}^N({{\mathbb {C}}})\) is called level-1 linearly non-degenerate if \({f_i}/{f_j}\) is a non-constant meromorphic function for any \(1 \leqslant i<j \leqslant N+1\) . We know that if f is linearly non-degenerate, then f is level-1 linearly non-degenerate. However, the converse is not true. In [8], the authors gave an answer for the Pakovich’s question (see [14]): under what conditions on subsets \( S, T \subset {{\mathbb {C}}\cup \{\infty \}} \) and two non-constant meromorphic functions f, g does the relation \(f ^ {- 1} (S) = g ^ {- 1}(T)\) holds? In this paper, we investigate this problem for level-1 linearly non-degenerate holomorphic mappings concerning hypersurfaces of Fermat-Yi type, namely, we introduce pairs of uniqueness hypersurfaces for powers of holomorphic mappings. Furthermore, we discuss some applications of the main result.
