I know that the quadratic reciprocity can be regarded as a special case of Artin reciprocity (class field theory), and we can get it by considering the cyclotomic extension of $\mathbb{Q}_{p}$. However, I want to know if there's any proof of quadratic reciprocity that doesn't use any stronger result, but only uses some properties of $p$-adic numbers. Thanks in advance.
2026-03-25 06:10:56.1774419056
Is there a proof of quadratic reciprocity using $p$-adic numbers?
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