完全数 (Chinese Wikipedia)

Analysis of information sources in references of the Wikipedia article "完全数" in Chinese language version.

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12web.archive.org

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9doi.org

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4harvard.edu

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2archive.org

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2books.google.com

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2arxiv.org

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2ams.org

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2byu.edu

1,687^th place

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1austms.org.au

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1oddperfect.org

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1worldcat.org

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1zbmath.org

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1lirmm.fr

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1colgate.edu

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1westga.edu

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1tus.ac.jp

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1swan.ac.uk

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ams.org

Iannucci, DE. The second largest prime divisor of an odd perfect number exceeds ten thousand (PDF). Mathematics of Computation. 1999, 68 (228): 1749–1760 [30 March 2011]. Bibcode:1999MaCom..68.1749I. doi:10.1090/S0025-5718-99-01126-6 . （原始内容 (PDF)存档于2021-11-03）.
Iannucci, DE. The third largest prime divisor of an odd perfect number exceeds one hundred (PDF). Mathematics of Computation. 2000, 69 (230): 867–879 [30 March 2011]. Bibcode:2000MaCom..69..867I. doi:10.1090/S0025-5718-99-01127-8. （原始内容存档 (PDF)于2013-05-17）.

archive.org

Dickson, L. E. History of the Theory of Numbers, Vol. I. Washington: Carnegie Institution of Washington. 1919: 10.
Dickson, L. E. History of the Theory of Numbers, Vol. I. Washington: Carnegie Institution of Washington. 1919: 25.

arxiv.org

Zelinsky, Joshua. Upper bounds on the second largest prime factor of an odd perfect number. International Journal of Number Theory. July 2019, 15 (6): 1183–1189. arXiv:1810.11734 . doi:10.1142/S1793042119500659. .
Nielsen, Pace P. Odd perfect numbers have at least nine distinct prime factors (PDF). Mathematics of Computation. 2007, 76 (260): 2109–2126 [30 March 2011]. Bibcode:2007MaCom..76.2109N. arXiv:math/0602485 . doi:10.1090/S0025-5718-07-01990-4. （原始内容 (PDF)存档于2021-11-03）.

austms.org.au

Roberts, T. On the Form of an Odd Perfect Number (PDF). Australian Mathematical Gazette. 2008, 35 (4): 244 [2021-03-15]. （原始内容存档 (PDF)于2013-05-14）.

books.google.com

Pickover, C. Wonders of Numbers: Adventures in Mathematics, Mind, and Meaning. Oxford: Oxford University Press. 2001: 360 [2021-11-08]. ISBN 0-19-515799-0. （原始内容存档于2022-03-22）.
Peterson, I. Mathematical Treks: From Surreal Numbers to Magic Circles. Washington: Mathematical Association of America. 2002: 132 [2021-11-08]. ISBN 88-8358-537-2. （原始内容存档于2021-11-08）.

byu.edu

math.byu.edu

Nielsen, Pace P. Odd perfect numbers, Diophantine equations, and upper bounds (PDF). Mathematics of Computation. 2015, 84 (295): 2549–2567 [13 August 2015]. doi:10.1090/S0025-5718-2015-02941-X . （原始内容 (PDF)存档于2015-07-08）.
Nielsen, Pace P. Odd perfect numbers have at least nine distinct prime factors (PDF). Mathematics of Computation. 2007, 76 (260): 2109–2126 [30 March 2011]. Bibcode:2007MaCom..76.2109N. arXiv:math/0602485 . doi:10.1090/S0025-5718-07-01990-4. （原始内容 (PDF)存档于2021-11-03）.

colgate.edu

math.colgate.edu

Zelinsky, Joshua. On the Total Number of Prime Factors of an Odd Perfect Number (PDF). Integers. 3 August 2021, 21 [7 August 2021]. （原始内容 (PDF)存档于2021-11-03）.

doi.org

Ochem, Pascal; Rao, Michaël. Odd perfect numbers are greater than 10¹⁵⁰⁰ (PDF). Mathematics of Computation. 2012, 81 (279): 1869–1877 [2021-11-03]. ISSN 0025-5718. Zbl 1263.11005. doi:10.1090/S0025-5718-2012-02563-4 . （原始内容 (PDF)存档于2016-01-15）.
Kühnel, Ullrich. Verschärfung der notwendigen Bedingungen für die Existenz von ungeraden vollkommenen Zahlen. Mathematische Zeitschrift. 1950, 52: 202–211. doi:10.1007/BF02230691 （德语）.
Goto, T; Ohno, Y. Odd perfect numbers have a prime factor exceeding 10⁸ (PDF). Mathematics of Computation. 2008, 77 (263): 1859–1868 [30 March 2011]. Bibcode:2008MaCom..77.1859G. doi:10.1090/S0025-5718-08-02050-9 . （原始内容 (PDF)存档于2011-08-07）.
Konyagin, Sergei; Acquaah, Peter. On Prime Factors of Odd Perfect Numbers. International Journal of Number Theory. 2012, 8 (6): 1537–1540. doi:10.1142/S1793042112500935.
Zelinsky, Joshua. Upper bounds on the second largest prime factor of an odd perfect number. International Journal of Number Theory. July 2019, 15 (6): 1183–1189. arXiv:1810.11734 . doi:10.1142/S1793042119500659. .
Iannucci, DE. The second largest prime divisor of an odd perfect number exceeds ten thousand (PDF). Mathematics of Computation. 1999, 68 (228): 1749–1760 [30 March 2011]. Bibcode:1999MaCom..68.1749I. doi:10.1090/S0025-5718-99-01126-6 . （原始内容 (PDF)存档于2021-11-03）.
Iannucci, DE. The third largest prime divisor of an odd perfect number exceeds one hundred (PDF). Mathematics of Computation. 2000, 69 (230): 867–879 [30 March 2011]. Bibcode:2000MaCom..69..867I. doi:10.1090/S0025-5718-99-01127-8. （原始内容存档 (PDF)于2013-05-17）.
Nielsen, Pace P. Odd perfect numbers, Diophantine equations, and upper bounds (PDF). Mathematics of Computation. 2015, 84 (295): 2549–2567 [13 August 2015]. doi:10.1090/S0025-5718-2015-02941-X . （原始内容 (PDF)存档于2015-07-08）.
Nielsen, Pace P. Odd perfect numbers have at least nine distinct prime factors (PDF). Mathematics of Computation. 2007, 76 (260): 2109–2126 [30 March 2011]. Bibcode:2007MaCom..76.2109N. arXiv:math/0602485 . doi:10.1090/S0025-5718-07-01990-4. （原始内容 (PDF)存档于2021-11-03）.

harvard.edu

ui.adsabs.harvard.edu

Goto, T; Ohno, Y. Odd perfect numbers have a prime factor exceeding 10⁸ (PDF). Mathematics of Computation. 2008, 77 (263): 1859–1868 [30 March 2011]. Bibcode:2008MaCom..77.1859G. doi:10.1090/S0025-5718-08-02050-9 . （原始内容 (PDF)存档于2011-08-07）.
Iannucci, DE. The second largest prime divisor of an odd perfect number exceeds ten thousand (PDF). Mathematics of Computation. 1999, 68 (228): 1749–1760 [30 March 2011]. Bibcode:1999MaCom..68.1749I. doi:10.1090/S0025-5718-99-01126-6 . （原始内容 (PDF)存档于2021-11-03）.
Iannucci, DE. The third largest prime divisor of an odd perfect number exceeds one hundred (PDF). Mathematics of Computation. 2000, 69 (230): 867–879 [30 March 2011]. Bibcode:2000MaCom..69..867I. doi:10.1090/S0025-5718-99-01127-8. （原始内容存档 (PDF)于2013-05-17）.
Nielsen, Pace P. Odd perfect numbers have at least nine distinct prime factors (PDF). Mathematics of Computation. 2007, 76 (260): 2109–2126 [30 March 2011]. Bibcode:2007MaCom..76.2109N. arXiv:math/0602485 . doi:10.1090/S0025-5718-07-01990-4. （原始内容 (PDF)存档于2021-11-03）.

lirmm.fr

Ochem, Pascal; Rao, Michaël. Odd perfect numbers are greater than 10¹⁵⁰⁰ (PDF). Mathematics of Computation. 2012, 81 (279): 1869–1877 [2021-11-03]. ISSN 0025-5718. Zbl 1263.11005. doi:10.1090/S0025-5718-2012-02563-4 . （原始内容 (PDF)存档于2016-01-15）.

oddperfect.org

存档副本. [2006-07-26]. （原始内容存档于2006-12-29）.

swan.ac.uk

www-maths.swan.ac.uk

[1]^{[永久失效連結]}

tus.ac.jp

ma.noda.tus.ac.jp

Goto, T; Ohno, Y. Odd perfect numbers have a prime factor exceeding 10⁸ (PDF). Mathematics of Computation. 2008, 77 (263): 1859–1868 [30 March 2011]. Bibcode:2008MaCom..77.1859G. doi:10.1090/S0025-5718-08-02050-9 . （原始内容 (PDF)存档于2011-08-07）.

web.archive.org

Pickover, C. Wonders of Numbers: Adventures in Mathematics, Mind, and Meaning. Oxford: Oxford University Press. 2001: 360 [2021-11-08]. ISBN 0-19-515799-0. （原始内容存档于2022-03-22）.
Peterson, I. Mathematical Treks: From Surreal Numbers to Magic Circles. Washington: Mathematical Association of America. 2002: 132 [2021-11-08]. ISBN 88-8358-537-2. （原始内容存档于2021-11-08）.
Roberts, T. On the Form of an Odd Perfect Number (PDF). Australian Mathematical Gazette. 2008, 35 (4): 244 [2021-03-15]. （原始内容存档 (PDF)于2013-05-14）.
存档副本. [2006-07-26]. （原始内容存档于2006-12-29）.
Ochem, Pascal; Rao, Michaël. Odd perfect numbers are greater than 10¹⁵⁰⁰ (PDF). Mathematics of Computation. 2012, 81 (279): 1869–1877 [2021-11-03]. ISSN 0025-5718. Zbl 1263.11005. doi:10.1090/S0025-5718-2012-02563-4 . （原始内容 (PDF)存档于2016-01-15）.
Zelinsky, Joshua. On the Total Number of Prime Factors of an Odd Perfect Number (PDF). Integers. 3 August 2021, 21 [7 August 2021]. （原始内容 (PDF)存档于2021-11-03）.
Nielsen, Pace P. An upper bound for odd perfect numbers. Integers. 2003, 3: A14–A22 [23 March 2021]. （原始内容存档于2003-02-21）.
Goto, T; Ohno, Y. Odd perfect numbers have a prime factor exceeding 10⁸ (PDF). Mathematics of Computation. 2008, 77 (263): 1859–1868 [30 March 2011]. Bibcode:2008MaCom..77.1859G. doi:10.1090/S0025-5718-08-02050-9 . （原始内容 (PDF)存档于2011-08-07）.
Iannucci, DE. The second largest prime divisor of an odd perfect number exceeds ten thousand (PDF). Mathematics of Computation. 1999, 68 (228): 1749–1760 [30 March 2011]. Bibcode:1999MaCom..68.1749I. doi:10.1090/S0025-5718-99-01126-6 . （原始内容 (PDF)存档于2021-11-03）.
Iannucci, DE. The third largest prime divisor of an odd perfect number exceeds one hundred (PDF). Mathematics of Computation. 2000, 69 (230): 867–879 [30 March 2011]. Bibcode:2000MaCom..69..867I. doi:10.1090/S0025-5718-99-01127-8. （原始内容存档 (PDF)于2013-05-17）.
Nielsen, Pace P. Odd perfect numbers, Diophantine equations, and upper bounds (PDF). Mathematics of Computation. 2015, 84 (295): 2549–2567 [13 August 2015]. doi:10.1090/S0025-5718-2015-02941-X . （原始内容 (PDF)存档于2015-07-08）.
Nielsen, Pace P. Odd perfect numbers have at least nine distinct prime factors (PDF). Mathematics of Computation. 2007, 76 (260): 2109–2126 [30 March 2011]. Bibcode:2007MaCom..76.2109N. arXiv:math/0602485 . doi:10.1090/S0025-5718-07-01990-4. （原始内容 (PDF)存档于2021-11-03）.

westga.edu

Nielsen, Pace P. An upper bound for odd perfect numbers. Integers. 2003, 3: A14–A22 [23 March 2021]. （原始内容存档于2003-02-21）.

worldcat.org

Ochem, Pascal; Rao, Michaël. Odd perfect numbers are greater than 10¹⁵⁰⁰ (PDF). Mathematics of Computation. 2012, 81 (279): 1869–1877 [2021-11-03]. ISSN 0025-5718. Zbl 1263.11005. doi:10.1090/S0025-5718-2012-02563-4 . （原始内容 (PDF)存档于2016-01-15）.

zbmath.org

Ochem, Pascal; Rao, Michaël. Odd perfect numbers are greater than 10¹⁵⁰⁰ (PDF). Mathematics of Computation. 2012, 81 (279): 1869–1877 [2021-11-03]. ISSN 0025-5718. Zbl 1263.11005. doi:10.1090/S0025-5718-2012-02563-4 . （原始内容 (PDF)存档于2016-01-15）.