Khác biệt giữa bản sửa đổi của “Định lý cơ bản của số học”

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{{tham khảo}}
==Sách tham khảo==
The ''[[Disquisitiones Arithmeticae]]'' has been translated from Latin into English and German. The German edition includes all of his papers on number theory: all the proofs of quadratic reciprocity, the determination of the sign of the Gauss sum, the investigations into biquadratic reciprocity, and unpublished notes.
* {{ citation | first1 = John B. | last1 = Fraleigh | year = 1976 | isbn = 0-201-01984-1 | title = A First Course In Abstract Algebra | edition = 2nd | publisher = [[Addison-Wesley]] | location = Reading }}
* {{citation
* {{ citation | first1 = I. N. | last1 = Herstein | author-link=Israel Nathan Herstein | year = 1964 | isbn = 978-1114541016 | title = Topics In Algebra | publisher = [[Blaisdell Publishing Company]] | location = Waltham }}
| last1 = Gauss | first1 = Carl Friedrich
* {{ citation | first1 = Calvin T. | last1 = Long | year = 1972 | title = Elementary Introduction to Number Theory | edition = 2nd | publisher = [[D. C. Heath and Company]] | location = Lexington | lccn = 77-171950 }}
| last2 = Clarke | first2 = Arthur A. (translator into English)
* {{ citation | first1 = Neal H. | last1 = McCoy | year = 1968 | title = Introduction To Modern Algebra, Revised Edition | publisher = [[Allyn and Bacon]] | location = Boston | lccn = 68-15225 }}
| title = Disquisitiones Arithemeticae (Second, corrected edition)
* {{ citation | first1 = Anthony J. | last1 = Pettofrezzo | first2 = Donald R. | last2 = Byrkit | year = 1970 | title = Elements of Number Theory | publisher = [[Prentice Hall]] | location = Englewood Cliffs | lccn = 77-81766 }}
| publisher = [[Springer Science+Business Media|Springer]]
| location = New York
| year = 1986
| isbn = 978-0-387-96254-2
| url = http://www.springer.com/mathematics/algebra/book/978-0-387-96254-2
}}
* {{citation
| last1 = Gauss | first1 = Carl Friedrich
| last2 = Maser | first2 = H. (translator into German)
| title = Untersuchungen über hohere Arithmetik (Disquisitiones Arithemeticae & other papers on number theory) (Second edition)
| publisher = Chelsea
| location = New York
| year = 1965
| isbn = 0-8284-0191-8}}
 
The two monographs Gauss published on biquadratic reciprocity have consecutively numbered sections: the first contains §§ 1–23 and the second §§ 24–76. Footnotes referencing these are of the form "Gauss, BQ, § ''n''". Footnotes referencing the ''Disquisitiones Arithmeticae'' are of the form "Gauss, DA, Art. ''n''".
* {{citation
| last1 = Gauss | first1 = Carl Friedrich
| title = Theoria residuorum biquadraticorum, Commentatio prima
| publisher = Comment. Soc. regiae sci, Göttingen 6
| location = Göttingen
| year = 1828}}
* {{citation
| last1 = Gauss | first1 = Carl Friedrich
| title = Theoria residuorum biquadraticorum, Commentatio secunda
| publisher = Comment. Soc. regiae sci, Göttingen 7
| location = Göttingen
| year = 1832}}
 
These are in Gauss's ''Werke'', Vol II, pp. 65–92 and 93–148; German translations are pp. 511–533 and 534–586 of the German edition of the ''Disquisitiones''.
* {{Citation
| last=Baker
| first=Alan
| author-link=
| year=1984
| title=A Concise Introduction to the Theory of Numbers
| place=Cambridge, UK
| publisher=Cambridge University Press
| isbn=978-0-521-28654-1
}}
* {{citation
| author1 = Euclid
| author1-link = Euclid
| others = Translated by [[Thomas Little Heath]]
| title = The thirteen books of the Elements
| edition = Second Edition Unabridged
| volume = 2 (Books III-IX)
| publisher = [[Dover]]
| location = New York
| year = 1956
| isbn = 978-0-486-60089-5
| url = http://store.doverpublications.com/0486600890.html
}}
* {{Hardy and Wright}}
* {{Citation
| author1 = A. Kornilowicz
| author2 = P. Rudnicki
| year = 2004
| title = Fundamental theorem of arithmetic
| journal = [[Formalized Mathematics]]
| volume = 12
| issue = 2
| pages = 179–185
}}
* {{citation
| first1 = Calvin T.
| last1 = Long
| year = 1972
| title = Elementary Introduction to Number Theory
| edition = 2nd | publisher = [[D. C. Heath and Company]]
| location = Lexington
| lccn = 77-171950
}}.
* {{citation
| first1 = Anthony J.
| last1 = Pettofrezzo
| first2 = Donald R.
| last2 = Byrkit
| year = 1970
| title = Elements of Number Theory
| publisher = [[Prentice Hall]]
| location = Englewood Cliffs
| lccn = 77-81766
}}.
* {{citation
| last1 = Riesel | first1 = Hans
| title = Prime Numbers and Computer Methods for Factorization (second edition)
| publisher = Birkhäuser
| location = Boston
| year = 1994
| isbn = 0-8176-3743-5}}
* {{mathworld|urlname=AbnormalNumber|title=Abnormal number}}
* {{mathworld|urlname=FundamentalTheoremofArithmetic|title=Fundamental Theorem of Arithmetic}}
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