Beal conjecture (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Beal conjecture" in English language version.

refsWebsite

Global rank English rank

18doi.org

2^nd place

12worldcat.org

5^th place

10arxiv.org

69^th place

59^th place

7semanticscholar.org

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8^th place

4ams.org

451^st place

277^th place

2web.archive.org

1^st place

2msp.org

low place

2harvard.edu

18^th place

17^th place

1bealconjecture.com

low place

1ubc.ca

1,997^th place

1,295^th place

1primepuzzles.net

low place

1archive.org

6^th place

1psu.edu

207^th place

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1yahoo.com

38^th place

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1sciencedirect.com

149^th place

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1uu.nl

2,467^th place

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1cambridge.org

305^th place

264^th place

1wisc.edu

1,045^th place

746^th place

1impan.pl

low place

1centre-mersenne.org

low place

1norvig.com

low place

1oeis.org

742^nd place

538^th place

1projecteuclid.org

3,707^th place

2,409^th place

1businessinsider.com

140^th place

115^th place

1isciencetimes.com

low place

1mathpuzzle.com

low place

ams.org

"Beal Conjecture". American Mathematical Society. Retrieved 21 August 2016.
R. Daniel Mauldin (1997). "A Generalization of Fermat's Last Theorem: The Beal Conjecture and Prize Problem" (PDF). Notices of the AMS. 44 (11): 1436–1439.
"Beal Prize". Ams.org. Retrieved 2014-03-06.
Chen, Imin (2007-10-23). "On the equation s₂+y^2p = α³". Mathematics of Computation. 77 (262): 1223–1228. doi:10.1090/S0025-5718-07-02083-2. ISSN 0025-5718.

archive.org

Crandall, Richard; Pomerance, Carl (2000). Prime Numbers: A Computational Perspective. Springer. p. 417. ISBN 978-0387-25282-7.

arxiv.org

Michel Waldschmidt (2004). "Open Diophantine Problems". Moscow Mathematical Journal. 4: 245–305. arXiv:math/0312440. doi:10.17323/1609-4514-2004-4-1-245-305. S2CID 11845578.
Poonen, Bjorn; Schaefer, Edward F.; Stoll, Michael (2005). "Twists of X(7) and primitive solutions to x² + y³ = z⁷". Duke Mathematical Journal. 137: 103–158. arXiv:math/0508174. Bibcode:2005math......8174P. doi:10.1215/S0012-7094-07-13714-1. S2CID 2326034.
Bruin, Nils (2005-03-01). "The primitive solutions to x³ + y⁹ = z²". Journal of Number Theory. 111 (1): 179–189. arXiv:math/0311002. doi:10.1016/j.jnt.2004.11.008. ISSN 0022-314X. S2CID 9704470.
Brown, David (2009). "Primitive Integral Solutions to x² + y³ = z¹⁰". arXiv:0911.2932 [math.NT].
Siksek, Samir; Stoll, Michael (2013). "The Generalised Fermat Equation x² + y³ = z¹⁵". Archiv der Mathematik. 102 (5): 411–421. arXiv:1309.4421. doi:10.1007/s00013-014-0639-z. S2CID 14582110.
Dahmen, Sander (2011). "A Refined Modular Approach to the Diophantie Equation x² + y²ⁿ = z³". International Journal of Number Theory. 7 (5): 1303–1316. arXiv:1002.0020. doi:10.1142/S1793042111004472. ISSN 1793-7310.
Siksek, Samir; Stoll, Michael (2012). "Partial descent on hyperelliptic curves and the generalized Fermat equation x³ + y⁴ + z⁵ = 0". Bulletin of the London Mathematical Society. 44 (1): 151–166. arXiv:1103.1979. doi:10.1112/blms/bdr086. ISSN 1469-2120. S2CID 12565749.
Dahmen, Sander R.; Siksek, Samir (2013). "Perfect powers expressible as sums of two fifth or seventh powers". arXiv:1309.4030 [math.NT].
Anni, Samuele; Siksek, Samir (2016-08-30). "Modular elliptic curves over real abelian fields and the generalized Fermat equation x^2ℓ + y^2m = z^p". Algebra & Number Theory. 10 (6): 1147–1172. arXiv:1506.02860. doi:10.2140/ant.2016.10.1147. ISSN 1944-7833. S2CID 118935511.
Billerey, Nicolas; Chen, Imin; Dembélé, Lassina; Dieulefait, Luis; Freitas, Nuno (2019-03-05). "Some extensions of the modular method and Fermat equations of signature (13, 13, n)". arXiv:1802.04330 [math.NT].

bealconjecture.com

"Beal Conjecture". Bealconjecture.com. Retrieved 2014-03-06.

businessinsider.com

Walter Hickey (5 June 2013). "If You Can Solve This Math Problem, Then A Texas Banker Will Give You $1 Million". Business Insider. Retrieved 8 July 2016.

cambridge.org

Freitas, Nuno; Naskręcki, Bartosz; Stoll, Michael (January 2020). "The generalized Fermat equation with exponents 2, 3, n". Compositio Mathematica. 156 (1): 77–113. doi:10.1112/S0010437X19007693. ISSN 0010-437X. S2CID 15030869.

centre-mersenne.org

jtnb.centre-mersenne.org

Bennett, Michael A. (2006). "The equation x²ⁿ + y²ⁿ = z⁵" (PDF). Journal de Théorie des Nombres de Bordeaux. 18 (2): 315–321. doi:10.5802/jtnb.546. ISSN 1246-7405.

doi.org

Michel Waldschmidt (2004). "Open Diophantine Problems". Moscow Mathematical Journal. 4: 245–305. arXiv:math/0312440. doi:10.17323/1609-4514-2004-4-1-245-305. S2CID 11845578.
Nitaj, Abderrahmane (1995). "On A Conjecture of Erdos on 3-Powerful Numbers". Bulletin of the London Mathematical Society. 27 (4): 317–318. CiteSeerX 10.1.1.24.563. doi:10.1112/blms/27.4.317.
Poonen, Bjorn; Schaefer, Edward F.; Stoll, Michael (2005). "Twists of X(7) and primitive solutions to x² + y³ = z⁷". Duke Mathematical Journal. 137: 103–158. arXiv:math/0508174. Bibcode:2005math......8174P. doi:10.1215/S0012-7094-07-13714-1. S2CID 2326034.
Bruin, Nils (2003-01-09). "Chabauty methods using elliptic curves". Journal für die reine und angewandte Mathematik. 2003 (562). doi:10.1515/crll.2003.076. ISSN 0075-4102.
Bruin, Nils (1999-09-01). "The diophantine equations x² ± y⁴ = ±z⁶ and x² + y⁸ = z³". Compositio Mathematica. 118 (3): 305–321. doi:10.1023/A:1001529706709 (inactive 1 November 2024). ISSN 0010-437X.{{cite journal}}: CS1 maint: DOI inactive as of November 2024 (link)
Bruin, Nils (2005-03-01). "The primitive solutions to x³ + y⁹ = z²". Journal of Number Theory. 111 (1): 179–189. arXiv:math/0311002. doi:10.1016/j.jnt.2004.11.008. ISSN 0022-314X. S2CID 9704470.
Freitas, Nuno; Naskręcki, Bartosz; Stoll, Michael (January 2020). "The generalized Fermat equation with exponents 2, 3, n". Compositio Mathematica. 156 (1): 77–113. doi:10.1112/S0010437X19007693. ISSN 0010-437X. S2CID 15030869.
Siksek, Samir; Stoll, Michael (2013). "The Generalised Fermat Equation x² + y³ = z¹⁵". Archiv der Mathematik. 102 (5): 411–421. arXiv:1309.4421. doi:10.1007/s00013-014-0639-z. S2CID 14582110.
Bennett, Michael A.; Chen, Imin (2012-07-25). "Multi-Frey $\mathbb {Q}$ -curves and the Diophantine equation a² + b⁶ = cⁿ". Algebra & Number Theory. 6 (4): 707–730. doi:10.2140/ant.2012.6.707. ISSN 1944-7833.
Chen, Imin (2007-10-23). "On the equation s₂+y^2p = α³". Mathematics of Computation. 77 (262): 1223–1228. doi:10.1090/S0025-5718-07-02083-2. ISSN 0025-5718.
Dahmen, Sander (2011). "A Refined Modular Approach to the Diophantie Equation x² + y²ⁿ = z³". International Journal of Number Theory. 7 (5): 1303–1316. arXiv:1002.0020. doi:10.1142/S1793042111004472. ISSN 1793-7310.
Siksek, Samir; Stoll, Michael (2012). "Partial descent on hyperelliptic curves and the generalized Fermat equation x³ + y⁴ + z⁵ = 0". Bulletin of the London Mathematical Society. 44 (1): 151–166. arXiv:1103.1979. doi:10.1112/blms/bdr086. ISSN 1469-2120. S2CID 12565749.
Poonen, Bjorn (1998). "Some diophantine equations of the form xⁿ + yⁿ = z^m". Acta Arithmetica (in Polish). 86 (3): 193–205. doi:10.4064/aa-86-3-193-205. ISSN 0065-1036.
Bennett, Michael A. (2006). "The equation x²ⁿ + y²ⁿ = z⁵" (PDF). Journal de Théorie des Nombres de Bordeaux. 18 (2): 315–321. doi:10.5802/jtnb.546. ISSN 1246-7405.
Anni, Samuele; Siksek, Samir (2016-08-30). "Modular elliptic curves over real abelian fields and the generalized Fermat equation x^2ℓ + y^2m = z^p". Algebra & Number Theory. 10 (6): 1147–1172. arXiv:1506.02860. doi:10.2140/ant.2016.10.1147. ISSN 1944-7833. S2CID 118935511.
Kraus, Alain (1998-01-01). "Sur l'équation a³ + b³ = c^p". Experimental Mathematics. 7 (1): 1–13. doi:10.1080/10586458.1998.10504355. ISSN 1058-6458.
Darmon, H.; Granville, A. (1995). "On the equations z^m = F(x, y) and Ax^p + By^q = Cz^r". Bulletin of the London Mathematical Society. 27 (6): 513–43. doi:10.1112/blms/27.6.513.
Rahimi, Amir M. (2017). "An Elementary Approach to the Diophantine Equation $ax^{m}+by^{n}=z^{r}$ Using Center of Mass". Missouri J. Math. Sci. 29 (2): 115–124. doi:10.35834/mjms/1513306825.

harvard.edu

dash.harvard.edu

Elkies, Noam D. (2007). "The ABC's of Number Theory" (PDF). The Harvard College Mathematics Review. 1 (1).

ui.adsabs.harvard.edu

Poonen, Bjorn; Schaefer, Edward F.; Stoll, Michael (2005). "Twists of X(7) and primitive solutions to x² + y³ = z⁷". Duke Mathematical Journal. 137: 103–158. arXiv:math/0508174. Bibcode:2005math......8174P. doi:10.1215/S0012-7094-07-13714-1. S2CID 2326034.

impan.pl

Poonen, Bjorn (1998). "Some diophantine equations of the form xⁿ + yⁿ = z^m". Acta Arithmetica (in Polish). 86 (3): 193–205. doi:10.4064/aa-86-3-193-205. ISSN 0065-1036.

isciencetimes.com

Times, Science (5 June 2013). "$1 Million Math Problem: Banker D. Andrew Beal Offers Award To Crack Conjecture Unsolved For 30 Years". International Science Times. Archived from the original on 29 September 2017.

mathpuzzle.com

"Neglected Gaussians". Mathpuzzle.com. Retrieved 2014-03-06.

msp.org

Bennett, Michael A.; Chen, Imin (2012-07-25). "Multi-Frey $\mathbb {Q}$ -curves and the Diophantine equation a² + b⁶ = cⁿ". Algebra & Number Theory. 6 (4): 707–730. doi:10.2140/ant.2012.6.707. ISSN 1944-7833.
Anni, Samuele; Siksek, Samir (2016-08-30). "Modular elliptic curves over real abelian fields and the generalized Fermat equation x^2ℓ + y^2m = z^p". Algebra & Number Theory. 10 (6): 1147–1172. arXiv:1506.02860. doi:10.2140/ant.2016.10.1147. ISSN 1944-7833. S2CID 118935511.

norvig.com

Norvig, Peter. "Beal's Conjecture: A Search for Counterexamples". Norvig.com. Retrieved 2014-03-06.

oeis.org

"Sloane's A261782 (see the Theorem and its proof in the comment from May 08 2021)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2021-06-19.

primepuzzles.net

"Mauldin / Tijdeman-Zagier Conjecture". Prime Puzzles. Retrieved 1 October 2016.

projecteuclid.org

Rahimi, Amir M. (2017). "An Elementary Approach to the Diophantine Equation $ax^{m}+by^{n}=z^{r}$ Using Center of Mass". Missouri J. Math. Sci. 29 (2): 115–124. doi:10.35834/mjms/1513306825.

psu.edu

citeseerx.ist.psu.edu

Nitaj, Abderrahmane (1995). "On A Conjecture of Erdos on 3-Powerful Numbers". Bulletin of the London Mathematical Society. 27 (4): 317–318. CiteSeerX 10.1.1.24.563. doi:10.1112/blms/27.4.317.

sciencedirect.com

Bruin, Nils (2005-03-01). "The primitive solutions to x³ + y⁹ = z²". Journal of Number Theory. 111 (1): 179–189. arXiv:math/0311002. doi:10.1016/j.jnt.2004.11.008. ISSN 0022-314X. S2CID 9704470.

semanticscholar.org

api.semanticscholar.org

Michel Waldschmidt (2004). "Open Diophantine Problems". Moscow Mathematical Journal. 4: 245–305. arXiv:math/0312440. doi:10.17323/1609-4514-2004-4-1-245-305. S2CID 11845578.
Poonen, Bjorn; Schaefer, Edward F.; Stoll, Michael (2005). "Twists of X(7) and primitive solutions to x² + y³ = z⁷". Duke Mathematical Journal. 137: 103–158. arXiv:math/0508174. Bibcode:2005math......8174P. doi:10.1215/S0012-7094-07-13714-1. S2CID 2326034.
Bruin, Nils (2005-03-01). "The primitive solutions to x³ + y⁹ = z²". Journal of Number Theory. 111 (1): 179–189. arXiv:math/0311002. doi:10.1016/j.jnt.2004.11.008. ISSN 0022-314X. S2CID 9704470.
Freitas, Nuno; Naskręcki, Bartosz; Stoll, Michael (January 2020). "The generalized Fermat equation with exponents 2, 3, n". Compositio Mathematica. 156 (1): 77–113. doi:10.1112/S0010437X19007693. ISSN 0010-437X. S2CID 15030869.
Siksek, Samir; Stoll, Michael (2013). "The Generalised Fermat Equation x² + y³ = z¹⁵". Archiv der Mathematik. 102 (5): 411–421. arXiv:1309.4421. doi:10.1007/s00013-014-0639-z. S2CID 14582110.
Siksek, Samir; Stoll, Michael (2012). "Partial descent on hyperelliptic curves and the generalized Fermat equation x³ + y⁴ + z⁵ = 0". Bulletin of the London Mathematical Society. 44 (1): 151–166. arXiv:1103.1979. doi:10.1112/blms/bdr086. ISSN 1469-2120. S2CID 12565749.
Anni, Samuele; Siksek, Samir (2016-08-30). "Modular elliptic curves over real abelian fields and the generalized Fermat equation x^2ℓ + y^2m = z^p". Algebra & Number Theory. 10 (6): 1147–1172. arXiv:1506.02860. doi:10.2140/ant.2016.10.1147. ISSN 1944-7833. S2CID 118935511.

ubc.ca

personal.math.ubc.ca

Bennett, Michael A.; Chen, Imin; Dahmen, Sander R.; Yazdani, Soroosh (June 2014). "Generalized Fermat Equations: A Miscellany" (PDF). Simon Fraser University. Retrieved 1 October 2016.

uu.nl

staff.science.uu.nl

Frits Beukers (January 20, 2006). "The generalized Fermat equation" (PDF). Staff.science.uu.nl. Retrieved 2014-03-06.

web.archive.org

"Billionaire Offers $1 Million to Solve Math Problem | ABC News Blogs – Yahoo". Gma.yahoo.com. 2013-06-06. Archived from the original on 2013-06-13. Retrieved 2014-03-06.
Times, Science (5 June 2013). "$1 Million Math Problem: Banker D. Andrew Beal Offers Award To Crack Conjecture Unsolved For 30 Years". International Science Times. Archived from the original on 29 September 2017.

wisc.edu

math.wisc.edu

"The Diophantine Equation" (PDF). Math.wisc.edu. Retrieved 2014-03-06.

worldcat.org

search.worldcat.org

Bruin, Nils (2003-01-09). "Chabauty methods using elliptic curves". Journal für die reine und angewandte Mathematik. 2003 (562). doi:10.1515/crll.2003.076. ISSN 0075-4102.
Bruin, Nils (1999-09-01). "The diophantine equations x² ± y⁴ = ±z⁶ and x² + y⁸ = z³". Compositio Mathematica. 118 (3): 305–321. doi:10.1023/A:1001529706709 (inactive 1 November 2024). ISSN 0010-437X.{{cite journal}}: CS1 maint: DOI inactive as of November 2024 (link)
Bruin, Nils (2005-03-01). "The primitive solutions to x³ + y⁹ = z²". Journal of Number Theory. 111 (1): 179–189. arXiv:math/0311002. doi:10.1016/j.jnt.2004.11.008. ISSN 0022-314X. S2CID 9704470.
Freitas, Nuno; Naskręcki, Bartosz; Stoll, Michael (January 2020). "The generalized Fermat equation with exponents 2, 3, n". Compositio Mathematica. 156 (1): 77–113. doi:10.1112/S0010437X19007693. ISSN 0010-437X. S2CID 15030869.
Bennett, Michael A.; Chen, Imin (2012-07-25). "Multi-Frey $\mathbb {Q}$ -curves and the Diophantine equation a² + b⁶ = cⁿ". Algebra & Number Theory. 6 (4): 707–730. doi:10.2140/ant.2012.6.707. ISSN 1944-7833.
Chen, Imin (2007-10-23). "On the equation s₂+y^2p = α³". Mathematics of Computation. 77 (262): 1223–1228. doi:10.1090/S0025-5718-07-02083-2. ISSN 0025-5718.
Dahmen, Sander (2011). "A Refined Modular Approach to the Diophantie Equation x² + y²ⁿ = z³". International Journal of Number Theory. 7 (5): 1303–1316. arXiv:1002.0020. doi:10.1142/S1793042111004472. ISSN 1793-7310.
Siksek, Samir; Stoll, Michael (2012). "Partial descent on hyperelliptic curves and the generalized Fermat equation x³ + y⁴ + z⁵ = 0". Bulletin of the London Mathematical Society. 44 (1): 151–166. arXiv:1103.1979. doi:10.1112/blms/bdr086. ISSN 1469-2120. S2CID 12565749.
Poonen, Bjorn (1998). "Some diophantine equations of the form xⁿ + yⁿ = z^m". Acta Arithmetica (in Polish). 86 (3): 193–205. doi:10.4064/aa-86-3-193-205. ISSN 0065-1036.
Bennett, Michael A. (2006). "The equation x²ⁿ + y²ⁿ = z⁵" (PDF). Journal de Théorie des Nombres de Bordeaux. 18 (2): 315–321. doi:10.5802/jtnb.546. ISSN 1246-7405.
Anni, Samuele; Siksek, Samir (2016-08-30). "Modular elliptic curves over real abelian fields and the generalized Fermat equation x^2ℓ + y^2m = z^p". Algebra & Number Theory. 10 (6): 1147–1172. arXiv:1506.02860. doi:10.2140/ant.2016.10.1147. ISSN 1944-7833. S2CID 118935511.
Kraus, Alain (1998-01-01). "Sur l'équation a³ + b³ = c^p". Experimental Mathematics. 7 (1): 1–13. doi:10.1080/10586458.1998.10504355. ISSN 1058-6458.

yahoo.com

gma.yahoo.com

"Billionaire Offers $1 Million to Solve Math Problem | ABC News Blogs – Yahoo". Gma.yahoo.com. 2013-06-06. Archived from the original on 2013-06-13. Retrieved 2014-03-06.