Gauss Lemma and Law of Quadratic Reciprocity

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Gauss Lemma and Law of Quadratic Reciprocity

In this paper, we defined the quadratic residue and proved its fundamental properties on the base of some useful theorems. Then we defined the Legendre symbol and proved its useful theorems [14], [12]. Finally, Gauss Lemma and Law of Quadratic Reciprocity are proven.

MML identifier: INT 5, version: 7.8.05 4.89.993

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  • [1] Grzegorz Bancerek. Cardinal numbers. Formalized Mathematics 1(2):377-382 1990.

  • [2] Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics 1(1):41-46 1990.

  • [3] Grzegorz Bancerek. König's theorem. Formalized Mathematics 1(3):589-593 1990.

  • [4] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics 1(1):91-96 1990.

  • [5] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics 1(1):107-114 1990.

  • [6] Czesław Byliński. Binary operations. Formalized Mathematics 1(1):175-180 1990.

  • [7] Czesław Byliński. Finite sequences and tuples of elements of a non-empty sets. Formalized Mathematics 1(3):529-536 1990.

  • [8] Czesław Byliński. Functions and their basic properties. Formalized Mathematics 1(1):55-65 1990.

  • [9] Czesław Byliński. Functions from a set to a set. Formalized Mathematics 1(1):153-164 1990.

  • [10] Czesław Byliński. The sum and product of finite sequences of real numbers. Formalized Mathematics 1(4):661-668 1990.

  • [11] Agata Darmochwał. Finite sets. Formalized Mathematics 1(1):165-167 1990.

  • [12] Zhang Dexin. Integer Theory. Science Publication China 1965.

  • [13] Yoshinori Fujisawa Yasushi Fuwa and Hidetaka Shimizu. Public-key cryptography and Pepin's test for the primality of Fermat numbers. Formalized Mathematics 7(2):317-321 1998.

  • [14] Hua Loo Keng. Introduction to Number Theory. Beijing Science Publication China 1957.

  • [15] Andrzej Kondracki. The Chinese Remainder Theorem. Formalized Mathematics 6(4):573-577 1997.

  • [16] Rafał Kwiatek. Factorial and Newton coefficients. Formalized Mathematics 1(5):887-890 1990.

  • [17] Rafał Kwiatek and Grzegorz Zwara. The divisibility of integers and integer relative primes. Formalized Mathematics 1(5):829-832 1990.

  • [18] Takaya Nishiyama and Yasuho Mizuhara. Binary arithmetics. Formalized Mathematics 4(1):83-86 1993.

  • [19] Dariusz Surowik. Cyclic groups and some of their properties - part I. Formalized Mathematics 2(5):623-627 1991.

  • [20] Michał J. Trybulec. Integers. Formalized Mathematics 1(3):501-505 1990.

  • [21] Zinaida Trybulec. Properties of subsets. Formalized Mathematics 1(1):67-71 1990.

  • [22] Edmund Woronowicz. Relations defined on sets. Formalized Mathematics 1(1):181-186 1990.

  • [23] Bo Zhang Hiroshi Yamazaki and Yatsuka Nakamura. Set sequences and monotone class. Formalized Mathematics 13(4):435-441 2005.

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CiteScore 2018: 0.42

SCImago Journal Rank (SJR) 2018: 0.111
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