I am working through Neukrich's Algebraic number theory book, and just read the chapter introducing the p-adics. At this stage we know the definition of the p-adics as the fraction field of the projective limit of $\mathbb{Z}/(p^n)$, a couple consequences of this defnition, and importantly nothing about the p-adic absolute value.
Yet exercise 2.1.5 of the book requires us to show $Aut(\mathbb{Q}_p)=\{Id\}$. I failed and so tried to search online for a solution, but they all use the p-adic absolute value, the density of $\mathbb{Q}$ and showing continuity of automorphisms. However given the place of this exercise, I am wondering whether anybody knows of any proof which doesn't require these techniques.
Thanks in advance.