Let $f_{1},f_{2},\ldots,f_{n}$ be different automorphisms of field $\mathbb{K}$ . What I want to ask is:
Does there exist an element $x \in \mathbb{K}$ such that $f_{1}(x),f_{2}(x),\ldots,f_{n}(x)$ are pairwise distinct?
Let $f_{1},f_{2},\ldots,f_{n}$ be different automorphisms of field $\mathbb{K}$ . What I want to ask is:
Does there exist an element $x \in \mathbb{K}$ such that $f_{1}(x),f_{2}(x),\ldots,f_{n}(x)$ are pairwise distinct?