Editing Euler's totient function (section)

==References==

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The ''[[Disquisitiones Arithmeticae]]'' has been translated from Latin into English and German. The German edition includes all of Gauss's 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reciprocity, the determination of the sign of the Gauss sum, the investigations into biquadratic reciprocity, and unpublished notes.

References to the ''Disquisitiones'' are of the form Gauss, DA, art. ''nnn''.

*{{citation
 | last1 = Abramowitz
 | first1 = M.
 | author1-link = Milton Abramowitz
 | last2 = Stegun
 | first2 = I. A.
 | author2-link = Irene A. Stegun
 | isbn = 0-486-61272-4
 | location = New York
 | publisher = [[Dover Publications]]
 | title = Handbook of Mathematical Functions
 | year = 1964
 | url = https://archive.org/details/handbookofmathe000abra
 }}. See paragraph 24.3.2.
*{{citation
 | last1 = Bach | first1 = Eric | author1-link = Eric Bach
 | last2 = Shallit | first2 = Jeffrey | author2-link = Jeffrey Shallit
 | title = Algorithmic Number Theory (Vol I: Efficient Algorithms)
 | publisher = [[The MIT Press]]
 | location = Cambridge, MA
 | year = 1996
 | isbn = 0-262-02405-5
 | zbl=0873.11070
 | series=MIT Press Series in the Foundations of Computing
}}
* Dickson, Leonard Eugene, "History Of The Theory Of Numbers", vol 1, chapter 5 "Euler's Function, Generalizations; Farey Series", Chelsea Publishing 1952
*{{citation
 | last = Ford | first = Kevin
 | doi = 10.2307/121103
 | mr = 1715326 | zbl=0978.11053
 | issn= 0003-486X
 | issue = 1
 | journal = [[Annals of Mathematics]]
 | jstor = 121103
 | pages = 283–311
 | title = The number of solutions of φ(''x'')&nbsp;=&nbsp;''m''
 | volume = 150
 | year = 1999}}.
*{{citation
 | last1 = Gauss | first1 = Carl Friedrich | author1-link = Carl Friedrich Gauss
 | translator-last = Clarke | translator-first = Arthur A. 
 | title = Disquisitiones Arithmeticae (Second, corrected edition)
 | publisher = [[Springer Publishing|Springer]]
 | location = New York
 | year = 1986
 | isbn = 0-387-96254-9}}
*{{citation
 | last1 = Gauss | first1 = Carl Friedrich | author1-link = Carl Friedrich Gauss
 | translator-last = Maser | translator-first = H. 
 | title = Untersuchungen uber hohere Arithmetik (Disquisitiones Arithmeticae & other papers on number theory) (Second edition)
 | publisher = Chelsea
 | location = New York
 | year = 1965
 | isbn = 0-8284-0191-8}}
*{{citation
 | last1 = Graham | first1 = Ronald | author1-link = Ronald Graham
 | last2 = Knuth | first2 = Donald | author2-link = Donald Knuth
 | last3 = Patashnik | first3 = Oren | author3-link = Oren Patashnik
 | title = [[Concrete Mathematics]]: a foundation for computer science
 | edition=2nd
 | publisher = Addison-Wesley
 | location = Reading, MA
 | year = 1994
 | isbn = 0-201-55802-5 | zbl=0836.00001}}
* {{citation | first=Richard K. | last=Guy | author-link=Richard K. Guy | title=Unsolved Problems in Number Theory | edition=3rd | publisher=[[Springer-Verlag]] | year=2004 | isbn=0-387-20860-7 | zbl=1058.11001 | series=Problem Books in Mathematics | location=New York, NY }}
*{{citation
 | last1 = Hardy | first1 = G. H. | author1-link = G. H. Hardy
 | last2 = Wright | first2 = E. M. | author2-link = E. M. Wright
 | title = [[An Introduction to the Theory of Numbers]]
 | edition = Fifth
 | publisher = [[Oxford University Press]]
 | location = Oxford
 | year = 1979
 | isbn = 978-0-19-853171-5}}
*{{citation
 | last = Liu | first = H.-Q.
 | journal = Proc. Roy. Soc. Edinburgh Sect. A
 | title = On Euler's function
 | volume = 146
 | issue = 4
 | year = 2016 | pages = 769–775
 | doi = 10.1017/S0308210515000682
 }}.
* {{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 = Ribenboim | first1 = Paulo | author-link = Paulo Ribenboim
 | title = The New Book of Prime Number Records | edition=3rd
 | publisher = [[Springer Science+Business Media|Springer]]
 | location = New York
 | year = 1996
 | zbl=0856.11001
 | isbn = 0-387-94457-5}}
*{{citation
 | last1 = Sandifer | first1 = Charles
 | title = The early mathematics of Leonhard Euler
 | publisher = MAA
 | year = 2007
 | isbn = 978-0-88385-559-1}}
* {{citation | editor1-last=Sándor | editor1-first=József | editor2-last=Mitrinović | editor2-first=Dragoslav S. | editor3-last=Crstici |editor3-first=Borislav | title=Handbook of number theory I | location=Dordrecht | publisher=[[Springer-Verlag]] | year=2006 | isbn=1-4020-4215-9 | zbl=1151.11300 | pages=9–36}}
* {{cite book | last1=Sándor | first1=Jozsef | last2=Crstici | first2=Borislav | title=Handbook of number theory II | url=https://archive.org/details/handbooknumberth00sand_741 | url-access=limited | location=Dordrecht | publisher=Kluwer Academic | year=2004 | isbn=1-4020-2546-7 | zbl=1079.11001 | pages=[https://archive.org/details/handbooknumberth00sand_741/page/n179 179]–327 }}
*{{citation
 | last = Schramm | first = Wolfgang
 | issue = 8(1)
 | journal = Electronic Journal of Combinatorial Number Theory
 | title = The Fourier transform of functions of the greatest common divisor
 | volume = A50
 | year = 2008
 |url=http://www.integers-ejcnt.org/vol8.html }}.
{{refend}}