If f(x) ∈ ℤ_p[x], a₀ ∈ ℤ_p with |f(a₀)| < |f'(a₀)|², then unique a ∈ ℤ_p with f(a)=0, a ≡ a₀ mod p. Newton's method over p-adics.
If f(x) ∈ ℤ_p[x], a₀ ∈ ℤ_p with |f(a₀)| < |f'(a₀)|², then unique a ∈ ℤ_p with f(a)=0, a ≡ a₀ mod p. Newton's method over p-adics.