Editing Number theory (section)

== References ==
{{reflist}}

=== Sources ===
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{{refbegin|30em}}
*{{citation |first=Joseph W. |last=Dauben |editor-last=Katz |editor-first=Victor J. |contribution=Chapter 3: Chinese Mathematics |pages=187–384 |publisher=Princeton University Press |year=2007 |title=The Mathematics of Egypt, Mesopotamia, China, India and Islam : A Sourcebook |isbn=978-0-691-11485-9}}
* {{cite book |last=Apostol |first=Tom M. |author-link=Tom M. Apostol |year=1976 |title=Introduction to analytic number theory |series=[[Undergraduate Texts in Mathematics]] |publisher=[[Springer Publishing|Springer]] |isbn=978-0-387-90163-3 |url=https://books.google.com/books?id=Il64dZELHEIC |access-date=2016-02-28}}
*{{citation |first=Ulrich |last=Libbrecht |title=Chinese Mathematics in the Thirteenth Century: the "Shu-shu Chiu-chang" of Ch'in Chiu-shao |publisher=Dover Publications Inc |isbn=978-0-486-44619-6 |date=1973}}
* {{cite journal |last=Apostol |first=Tom M. |year=1981 |title=An Introduction to the Theory of Numbers (Review of Hardy & Wright.) |journal=Mathematical Reviews (MathSciNet) |mr=0568909 |publisher=[[American Mathematical Society]]}} (Subscription needed)
* {{cite journal |last=Becker |first=Oskar |year=1936 |author-link=Oskar Becker |language=de |title=Die Lehre von Geraden und Ungeraden im neunten Buch der euklidischen Elemente |journal=Quellen und Studien zur Geschichte der Mathematik, Astronomie und Physik |series=Abteilung B:Studien |volume=3 |pages=533–553}}
* {{cite book |last1=Boyer |first1=Carl Benjamin |last2=Merzbach |first2=Uta C. |author2-link=Uta Merzbach |year=1991 |author-link=Carl Benjamin Boyer |title=A History of Mathematics |edition=2nd |orig-year=1968 |location=New York |publisher=[[Wiley (publisher)|Wiley]] |isbn=978-0-471-54397-8 |url=https://archive.org/details/historyofmathema00boye}} [https://archive.org/details/AHistoryOfMathematics 1968 edition] at archive.org
* {{cite book |author=Aryabhata |translator-last=Clark |translator-first=Walter Eugene |ref={{sfnref|Clark|1930}} |author-link=Aryabhata |year=1930 |title=The Āryabhaṭīya of Āryabhaṭa: An ancient Indian work on Mathematics and Astronomy |publisher=[[University of Chicago Press]] |url=https://archive.org/details/The_Aryabhatiya_of_Aryabhata_Clark_1930 |access-date=2016-02-28}}
* {{cite book |last=Colebrooke |first=Henry Thomas |year=1817 |author-link=Henry Thomas Colebrooke |title=Algebra, with Arithmetic and Mensuration, from the Sanscrit of Brahmegupta and Bháscara |location=London |publisher=J. Murray |url=https://archive.org/details/algebrawitharith00brahuoft |access-date=2016-02-28}}
* {{cite book |last1=Davenport |first1=Harold |author-link=Harold Davenport |year=2000 |last2=Montgomery |first2=Hugh L. |author2-link=Hugh Montgomery (mathematician) |title=Multiplicative Number Theory |edition=revised 3rd |series=Graduate Texts in Mathematics |volume=74 |publisher=[[Springer Publishing|Springer]] |isbn=978-0-387-95097-6}}
* {{cite journal |last=Edwards |first=Harold M. |author-link=Harold Edwards (mathematician) |date=November 1983 |title=Euler and Quadratic Reciprocity |journal=Mathematics Magazine |volume=56 |issue=5 |pages=285–291 |doi=10.2307/2690368 |jstor=2690368}}
* {{cite book |last=Edwards |first=Harold M. |year=2000 |orig-year=1977 |title=Fermat's Last Theorem: a Genetic Introduction to Algebraic Number Theory |edition=reprint of 1977 |series=Graduate Texts in Mathematics |volume=50 |publisher=[[Springer Verlag]] |isbn=978-0-387-95002-0 |url=https://books.google.com/books?id=_IxN-5PW8asC}}
* {{cite book |last=Fermat |first=Pierre de |year=1679 |author-link=Pierre de Fermat |language=fr, la |title=Varia Opera Mathematica |location=Toulouse |publisher=Joannis Pech |url=https://archive.org/details/bub_gb_fvZaAAAAQAAJ |access-date=2016-02-28}}
* {{cite journal |last=Friberg |first=Jöran |date=August 1981 |title=Methods and Traditions of Babylonian Mathematics: Plimpton 322, Pythagorean Triples and the Babylonian Triangle Parameter Equations |journal=Historia Mathematica |volume=8 |issue=3 |pages=277–318 |doi=10.1016/0315-0860(81)90069-0 |doi-access=free}}
* {{cite book |last=von Fritz |first=Kurt |editor1-last=Christianidis |editor1-first=J. |year=2004 |chapter=The Discovery of Incommensurability by Hippasus of Metapontum |title=Classics in the History of Greek Mathematics |location=Berlin |publisher=Kluwer (Springer) |isbn=978-1-4020-0081-2}}
* {{cite book |last1=Gauss |ref={{harvid|Gauss, Disqu. Arith.||}} |first1=Carl Friedrich |translator-last=Waterhouse |translator-first=William C. |year=1966 |author-link=Carl Friedrich Gauss |title=Disquisitiones Arithmeticae |orig-year=1801 |publisher=Springer |isbn=978-0-387-96254-2 |url=https://books.google.com/books?id=8LcK_CwzMpQC}}
* {{cite web |last=Goldfeld |first=Dorian M. |author-link=Dorian M. Goldfeld |year=2003 |title=Elementary Proof of the Prime Number Theorem: a Historical Perspective |url=http://www.math.columbia.edu/~goldfeld/ErdosSelbergDispute.pdf |access-date=2016-02-28 |archive-date=2016-03-03 |archive-url=https://web.archive.org/web/20160303234413/http://www.math.columbia.edu/~goldfeld/ErdosSelbergDispute.pdf |url-status=live}}
* {{cite book |last1=Goldstein |first1=Catherine |author-link=Catherine Goldstein |last2=Schappacher |first2=Norbert |year=2007 |editor1-last=Goldstein |editor1-first=C. |editor2-last=Schappacher |editor2-first=N. |editor3-last=Schwermer |editor3-first=Joachim |chapter=A book in search of a discipline |title=The Shaping of Arithmetic after C.F. Gauss's "Disquisitiones Arithmeticae" |location=Berlin & Heidelberg |publisher=Springer |isbn=978-3-540-20441-1 |chapter-url=https://books.google.com/books?id=IUFTcOsMTysC |pages=3–66 |access-date=2016-02-28}}
* {{cite book |last=Granville |first=Andrew |author-link=Andrew Granville |year=2008 |editor1-last=Gowers |editor1-first=Timothy |editor1-link=Timothy Gowers |editor2-last=Barrow-Green |editor2-first=June |editor3-last=Leader |editor3-first=Imre |editor3-link=Imre Leader |chapter=Analytic number theory |title=The Princeton Companion to Mathematics |publisher=[[Princeton University Press]] |isbn=978-0-691-11880-2 |chapter-url=https://books.google.com/books?id=ZOfUsvemJDMC&pg=PA332 |access-date=2016-02-28 |title-link=The Princeton Companion to Mathematics}}
* {{cite book |ref={{harvid|Guthrie|1920}} |translator-last=Guthrie |translator-first=K. S. |translator-link=Kenneth Sylvan Guthrie |year=1920 |last1=Porphyry |author1-link=Porphyry (philosopher) |title=Life of Pythagoras |location=Alpine, New Jersey |publisher=Platonist Press |url=http://www.tertullian.org/fathers/porphyry_life_of_pythagoras_02_text.htm |access-date=2012-04-10 |archive-date=2020-02-29 |archive-url=https://web.archive.org/web/20200229061904/http://www.tertullian.org/fathers/porphyry_life_of_pythagoras_02_text.htm |url-status=live}}
* {{cite book |last=Guthrie |first=Kenneth Sylvan |year=1987 |author-link=Kenneth Sylvan Guthrie |title=The Pythagorean Sourcebook and Library |location=Grand Rapids, Michigan |publisher=Phanes Press |isbn=978-0-933999-51-0}}
* {{Cite book |last1=Hardy |first1=Godfrey Harold |author1-link=G. H. Hardy |last2=Wright |first2=E. M. |title=An Introduction to the Theory of Numbers |orig-year=1938 |publisher=[[Oxford University Press]] |edition=6th |isbn=978-0-19-921986-5 |mr=2445243 |year=2008 |title-link=An Introduction to the Theory of Numbers}}
* {{cite book |last=Heath |first=Thomas L. |year=1921 |author-link=Thomas Little Heath |title=A History of Greek Mathematics, Volume 1: From Thales to Euclid |location=Oxford |publisher=[[Clarendon Press]] |url=https://archive.org/details/historyofgreekma01heat |access-date=2016-02-28}}
<!-- Alternative Info – Google limited preview
 |year=1981
 |publisher=Courier Dover Publications
 |url=https://books.google.com/books?id=drnY3Vjix3kC
 |isbn=0-486-24073-8, 9780486240732 -->
* {{cite book |last=Hopkins |first=J. F. P. |editor1-last=Young |editor1-first=M. J. L. |editor2-last=Latham |editor2-first=J. D. |editor3-last=Serjeant |editor3-first=R. B. |year=1990 |chapter=Geographical and Navigational Literature |title=Religion, Learning and Science in the 'Abbasid Period |series=The Cambridge history of Arabic literature |publisher=[[Cambridge University Press]] |isbn=978-0-521-32763-3}}
* {{cite encyclopedia |last=Huffman |first=Carl A. |editor1-last=Zalta |editor1-first=Edward N. |date=8 August 2011 |title=Pythagoras |encyclopedia=Stanford Encyclopaedia of Philosophy |edition=Fall 2011 |url=http://plato.stanford.edu/archives/fall2011/entries/pythagoras/ |access-date=7 February 2012 |archive-date=2 December 2013 |archive-url=https://web.archive.org/web/20131202071830/http://plato.stanford.edu/archives/fall2011/entries/pythagoras/ |url-status=live}}
* {{cite book |last1=Iwaniec |first1=Henryk |author-link=Henryk Iwaniec |last2=Kowalski |first2=Emmanuel |year=2004 |title=Analytic Number Theory |series=American Mathematical Society Colloquium Publications |volume=53 |location=Providence, RI |publisher=American Mathematical Society |isbn=978-0-8218-3633-0}}
* {{cite book |ref={{harvid|Jowett|1871}} |translator-last=Jowett |translator-first=Benjamin |translator-link=Benjamin Jowett |year=1871 |last1=Plato |author1-link=Plato |title=Theaetetus |url=http://classics.mit.edu/Plato/theatu.html |access-date=2012-04-10 |archive-date=2011-07-09 |archive-url=https://web.archive.org/web/20110709194524/http://classics.mit.edu/Plato/theatu.html |url-status=live}}
* {{cite book |last1=Lam |first1=Lay Yong |last2=Ang |first2=Tian Se |year=2004 |author-link=Lam Lay Yong |title=Fleeting Footsteps: Tracing the Conception of Arithmetic and Algebra in Ancient China |edition=revised |location=Singapore |publisher=World Scientific |isbn=978-981-238-696-0 |url=https://books.google.com/books?id=fGYmpWE5UZgC |access-date=2016-02-28}}
* {{ cite book |last=Long |first=Calvin T. |year=1972 |title=Elementary Introduction to Number Theory |edition=2nd |publisher=[[D.C. Heath and Company]] |location=Lexington, VA |lccn=77171950}}
* {{cite book |last=Mahoney |first=M. S. |year=1994 |title=The Mathematical Career of Pierre de Fermat, 1601–1665 |edition=Reprint, 2nd |publisher=[[Princeton University Press]] |isbn=978-0-691-03666-3 |url=https://books.google.com/books?id=My19IcewAnoC |access-date=2016-02-28}}
* {{cite web
<!--{{sfn|Milne|2014|p=}} -->
|last=Milne
|first=J. S.
|author-link=James Milne (mathematician)
|date=18 March 2017
|issue=3.07
|title=Algebraic Number Theory
|url=https://www.jmilne.org/math/CourseNotes/ant.html
|access-date=7 April 2020}}
* {{cite book |last1=Montgomery |first1=Hugh L. |author-link=Hugh Montgomery (mathematician) |year=2007 |last2=Vaughan |first2=Robert C. |author2-link=Bob Vaughan |title=Multiplicative Number Theory: I, Classical Theory |publisher=Cambridge University Press |isbn=978-0-521-84903-6 |url=https://books.google.com/books?id=nGb1NADRWgcC |access-date=2016-02-28}}
* {{cite book |ref={{harvid|Morrow|1992}} |translator-last=Morrow |translator-first=Glenn Raymond |author=Euclid |year=1992 |last2=Proclus |author2-link=Proclus |title=A Commentary on Book 1 of Euclid's Elements |publisher=Princeton University Press |isbn=978-0-691-02090-7 |url=https://books.google.com/books?id=JZEHj2fEmqAC&pg=PA52}}
* {{cite journal |last=Mumford |first=David |author-link=David Mumford |title=Mathematics in India: reviewed by David Mumford |journal=Notices of the American Mathematical Society |date=March 2010 |volume=57 |issue=3 |page=387 |issn=1088-9477 |url=https://www.ams.org/notices/201003/rtx100300385p.pdf |access-date=2021-04-28 |archive-date=2021-05-06 |archive-url=https://web.archive.org/web/20210506220302/https://www.ams.org/notices/201003/rtx100300385p.pdf |url-status=live}}
* {{cite book |last=Neugebauer |first=Otto E. |year=1969 |author-link=Otto E. Neugebauer |title=The Exact Sciences in Antiquity |volume=9 |location=New York |publisher=Dover Publications |isbn=978-0-486-22332-2}}
* {{cite book |ref={{harvid|Neugebauer|Sachs|1945}} |last1=Neugebauer |first1=Otto E. |last2=Sachs |first2=Abraham Joseph |last3=Götze |first3=Albrecht |year=1945 |author-link=Otto E. Neugebauer |author2-link=Abraham Sachs |title=Mathematical Cuneiform Texts |series=American Oriental Series |volume=29 |publisher=[[American Oriental Society]] etc.}}
* {{cite web |last=O'Grady |first=Patricia |author-link=Patricia O'Grady |date=September 2004 |title=Thales of Miletus |url=http://www.iep.utm.edu/thales/ |publisher=The Internet Encyclopaedia of Philosophy |access-date=7 February 2012 |archive-date=6 January 2016 |archive-url=https://web.archive.org/web/20160106182825/http://www.iep.utm.edu/thales/ |url-status=live}}
* {{cite journal |ref={{harvid|Pingree|1968}} |last1=Pingree |first1=David |last2=Ya'qub |first2=ibn Tariq |author1-link=David Pingree |author2-link=Yaʿqūb ibn Ṭāriq |year=1968 |title=The Fragments of the Works of Ya'qub ibn Tariq |journal=Journal of Near Eastern Studies |volume=26}}
* {{cite journal |ref={{harvid|Pingree|1970}} |last1=Pingree |first1=D. |author1-link=David Pingree |last2=al-Fazari |year=1970 |author2-link=al-Fazari |title=The Fragments of the Works of al-Fazari |journal=Journal of Near Eastern Studies |volume=28}}
* {{cite book |last=Plofker |first=Kim |author-link=Kim Plofker |year=2008 |title=Mathematics in India |title-link=Mathematics in India (book) |publisher=Princeton University Press |isbn=978-0-691-12067-6}}
* {{cite book |editor1-last=Qian |editor1-first=Baocong |year=1963 |language=zh |title=Suanjing shi shu (Ten Mathematical Classics) |location=Beijing |publisher=Zhonghua shuju |url=https://www.scribd.com/doc/53797787/Jigu-Suanjing%E3%80%80%E7%B7%9D%E5%8F%A4%E7%AE%97%E7%B6%93-Qian-Baocong-%E9%8C%A2%E5%AF%B6%E7%90%AE |access-date=2016-02-28 |archive-date=2013-11-02 |archive-url=https://web.archive.org/web/20131102154812/http://www.scribd.com/doc/53797787/Jigu-Suanjing%E3%80%80%E7%B7%9D%E5%8F%A4%E7%AE%97%E7%B6%93-Qian-Baocong-%E9%8C%A2%E5%AF%B6%E7%90%AE |url-status=live}}
* {{cite journal |last=Rashed |first=Roshdi |year=1980 |title=Ibn al-Haytham et le théorème de Wilson |journal=Archive for History of Exact Sciences |volume=22 |issue=4 |pages=305–321 |doi=10.1007/BF00717654 |s2cid=120885025}}
* {{cite journal |last=Robson |first=Eleanor |author-link=Eleanor Robson |year=2001 |title=Neither Sherlock Holmes nor Babylon: a Reassessment of Plimpton 322 |volume=28 |journal=Historia Mathematica |issue=3 |pages=167–206 |doi=10.1006/hmat.2001.2317 |url=http://www.hps.cam.ac.uk/people/robson/neither-sherlock.pdf |archive-url=https://web.archive.org/web/20141021070742/http://www.hps.cam.ac.uk/people/robson/neither-sherlock.pdf |archive-date=2014-10-21}}
* {{cite book |last1=Sachau |first1=Eduard |author-link=Eduard Sachau |last2=Bīrūni |first2=̄Muḥammad ibn Aḥmad |author2-link=Abū Rayḥān al-Bīrūnī |year=1888 |title=Alberuni's India: An Account of the Religion, Philosophy, Literature, Geography, Chronology, Astronomy and Astrology of India, Vol. 1 |location=London |publisher=Kegan, Paul, Trench, Trübner & Co. |url=http://onlinebooks.library.upenn.edu/webbin/book/lookupname?key=Sachau%2C%20Eduard%2C%201845-1930 |access-date=2016-02-28 |archive-date=2016-03-03 |archive-url=https://web.archive.org/web/20160303235035/http://onlinebooks.library.upenn.edu/webbin/book/lookupname?key=Sachau,%20Eduard,%201845-1930 |url-status=live}}
* {{cite book |last=Serre |first=Jean-Pierre |year=1996 |orig-year=1973 |author-link=Jean-Pierre Serre |title=A Course in Arithmetic |series=Graduate Texts in Mathematics |volume=7 |publisher=[[Springer Publishing|Springer]] |isbn=978-0-387-90040-7 |url=https://archive.org/details/courseinarithmet00serr}}
* {{cite book |last=Smith |first=D. E. |year=1958 |title=History of Mathematics, Vol I |location=New York |publisher=Dover}}
* {{cite book |ref={{harvid|Tannery|Henry|1891}} |last1=Tannery |first1=Paul |author1-link=Paul Tannery |editor1=Charles Henry |editor1-link=Charles Henry (librarian) |year=1891 |last2=Fermat |first2=Pierre de |author2-link=Pierre de Fermat |language=fr, la |title=Oeuvres de Fermat |series=(4 Vols.) |location=Paris |publisher=Imprimerie Gauthier-Villars et Fils |url=https://archive.org/details/oeuvresdefermat01ferm}} [https://archive.org/details/oeuvresdefermat01ferm Volume 1] [https://archive.org/details/oeuvresdefermat02ferm Volume 2] [https://archive.org/details/oeuvresdefermat03ferm Volume 3] [https://archive.org/details/oeuvresdefermat04ferm Volume 4 (1912)]
* {{cite book |ref={{harvid|Taylor|1818}} |translator-last=Taylor |translator-first=Thomas |translator-link=Thomas Taylor (neoplatonist) |year=1818 |author1=Iamblichus |author1-link=Iamblichus |title=Life of Pythagoras or, Pythagoric Life |location=London |publisher=J. M. Watkins}} For other editions, see [[Iamblichus#List of editions and translations]]
* {{cite book |last=Truesdell |first=C. A. |author-link=Clifford Truesdell |year=1984 |translator-last=Hewlett |translator-first=John |chapter=Leonard Euler, Supreme Geometer |title=Leonard Euler, Elements of Algebra |edition=reprint of 1840 5th |location=New York |publisher=[[Springer-Verlag]] |isbn=978-0-387-96014-2 |chapter-url=https://books.google.com/books?id=mkOhy6v7kIsC}} This Google books preview of ''Elements of algebra'' lacks Truesdell's intro, which is reprinted (slightly abridged) in the following book:
* {{cite book |last=Truesdell |first=C. A. |author-link=Clifford Truesdell |year=2007 |editor1-last=Dunham |editor1-first=William |chapter=Leonard Euler, Supreme Geometer |title=The Genius of Euler: reflections on his life and work |series=Volume 2 of MAA tercentenary Euler celebration |location=New York |publisher=[[Mathematical Association of America]] |isbn=978-0-88385-558-4 |chapter-url=https://books.google.com/books?id=M4-zUnrSxNoC |access-date=2016-02-28}}
* {{cite book |last=Varadarajan |first=V. S. |year=2006 |title=Euler Through Time: A New Look at Old Themes |publisher=[[American Mathematical Society]] |isbn=978-0-8218-3580-7 |url=https://books.google.com/books?id=CYyKTREGYd0C |access-date=2016-02-28}}
* {{cite journal |last=Vardi |first=Ilan |title=Archimedes' Cattle Problem |date=April 1998 |journal=American Mathematical Monthly |volume=105 |issue=4 |pages=305–319 |doi=10.2307/2589706 |url=https://www.cs.drexel.edu/~crorres/Archimedes/Cattle/cattle_vardi.pdf |jstor=2589706 |citeseerx=10.1.1.383.545 |access-date=2012-04-08 |archive-date=2012-07-15 |archive-url=https://web.archive.org/web/20120715031904/https://www.cs.drexel.edu/~crorres/Archimedes/Cattle/cattle_vardi.pdf |url-status=live}}
* {{cite book |last1=van der Waerden |first1=Bartel L. |translator-last=Dresden |translator-first=Arnold |year=1961 |author-link=Bartel Leendert van der Waerden |title=Science Awakening |volume=1 or 2 |location=New York |publisher=[[Oxford University Press]]}}
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url=https://books.google.com/books?id=S_T6Pt2qZ5YC&
Translated by Peter Huber
Publisher Springer, 1974
{{isbn|90-01-93103-0}}, {{isbn|978-90-01-93103-2}} -->
* {{cite book |last=Weil |first=André |year=1984 |author-link=André Weil |title=Number Theory: an Approach Through History – from Hammurapi to Legendre |location=Boston |publisher=Birkhäuser |isbn=978-0-8176-3141-3 |url=https://books.google.com/books?id=XSV0hDFj3loC |access-date=2016-02-28}}
{{refend}}
* {{Citizendium}}