A Proof of the Gauss Quadratic Reciprocity Law

Darafsheh, M. R.

doi:10.30504/mct.2023.1239.1863

A Proof of the Gauss Quadratic Reciprocity Law

Document Type : Original

Author

M. R. Darafsheh

School of Mathematics, Statistics and Computer Science, University of Tehran, Iran

10.30504/mct.2023.1239.1863

Abstract

The Gauss quadratic reciprocity law is one of the most important theorems
in number theory which Gauss proved it in nineteen years old. In this paper, we first
prove some facts about the character of finite abelian groups. Then, using them, we
provide a proof for the Gauss quadratic reciprocity law.

Keywords

the law of quadratic reciprocity

character on finite group

Legendre symbol

20.1001.1.10226443.1401.41.2.5.4

Subjects

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