$$P(x, y)=0 \tag {1} \\ \text{ where }P(x, y) \in \mathbb{Q}[x, y]$$
How do we know that $(1)$ has a solution in a $\mathbb{Q}_p$ ?
We will apply Hensel's Lemma.
Idea: we begin from an element of $\mathbb{Q}_p$, that has some identities $(a_1)$.
Then we create a sequence of values $a_1, a_2, \dots$ that approaches the root, that we finally find.
Hensel's Lemma gives us the most important algebraic identity of $\mathbb{Q}_p$.
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At the beginning of the idea, we have that:
"we begin from an element of $\mathbb{Q}_p$, that has some identities $(a_1)$"
What identities are meant??