Gauss Lemma and Law of Quadratic Reciprocity
Li Yan ; Xiquan Liang ; Junjie Zhao
Formalized Mathematics, Tome 16 (2008), p. 23-28 / Harvested from The Polish Digital Mathematics Library
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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

Publié le : 2008-01-01
EUDML-ID : urn:eudml:doc:266986 
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     title = {Gauss Lemma and Law of Quadratic Reciprocity},
     journal = {Formalized Mathematics},
     volume = {16},
     year = {2008},
     pages = {23-28},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_v10037-008-0004-4}
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Li Yan; Xiquan Liang; Junjie Zhao. Gauss Lemma and Law of Quadratic Reciprocity. Formalized Mathematics, Tome 16 (2008) pp. 23-28. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_v10037-008-0004-4/

[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. | Zbl 06213858

[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.