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proofs of quadratic reciprocity
In number theory, the law of quadratic reciprocity, like the Pythagorean theorem, has lent itself to an unusual number of proofs. Several hundred proofs of the law of quadratic reciprocity have been found.
==Proofs that are accessible==
Of relatively elementary, combinatorial proofs, there are two which apply types of double counting. One by Gotthold Eisenstein counts lattice points. Another applies Zolotarev's lemma to ''Z''/''pqZ'' expressed by the Chinese remainder theorem as ''Z''/''pZ''×''Z''/''qZ'', and calculates the signature of a permutation.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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