A Variation of Takagi's Proof for Quadratic Reciprocity Laws for Jacobi Symbols

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Abstract

It is well known that Gauss has found the first complete proof of quadratic reciprocity laws in [2] (1801) and many different proofs for quadratic reciprocity laws of Legendre symbols have been published after then (see for example Appendix B of Lemmermeyer’s text [11]). In this paper, we shall write down a visual proof of quadratic reciprocity laws for Jacobi symbols depending on Schering’s generalization of Gauss’s lemma.

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