Prove that an absolute value \(|\cdot|\) on a field \(k\) is nonarchimedean if and only if \(|n|\leq 1\) for all \(n\in\mathbb{Z}_{>0}\) (view \(n\) as an element of \(k\) via the canonical ring homomorphism \(\mathbb{Z}\to k\)). (Hint: use the binomial theorem).