数学 LaTeX测试帖
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$[拓]一些小小的性质：
1. $ v_p(xy) =$$ v_p(x) +$$ v_p(y) $
2. $ v_p(x + y) $$ \geq \min(v_p(x), v_p(y)) $，当 $ v_p(x) $$\ne$$ v_p(y) $等号成立
3. $ v_p(x) \geq 0 $ 当且仅当 $ x \in \mathbb{Z}_p $（p进整数）
4. $ v_p(n!) = \sum_{i=1}^\infty$ \left\lfloor$ \frac{n}{p^i}$ \right\rfloor $
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