Geodesic
On the equation $a^{3} + b^{3n} = c^{2}$
Michael A. Bennett1 ; Imin Chen2 ; Sander R. Dahmen3 ; Soroosh Yazdani4
1 Department of Mathematics University of British Columbia Vancouver, British Columbia, V6T 1Z2, Canada
2 Department of Mathematics Simon Fraser University Burnaby, British Columbia, Canada
3 Department of Mathematics VU University Amsterdam De Boelelaan 1081a 1081 HV Amsterdam, The Netherlands
4 Department of Mathematics and Computer Science University of Lethbridge Lethbridge, Alberta, T1K 3M4, Canada
Acta Arithmetica, Tome 163 (2014) no. 4, pp. 327-343.

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We study coprime integer solutions to the equation $a^3 + b^{3n} = c^2$ using Galois representations and modular forms. This case represents perhaps the last natural family of generalized Fermat equations descended from spherical cases which is amenable to resolution using the so-called modular method. Our techniques involve an elaborate combination of ingredients, ranging from $\mathbb Q$-curves and a delicate multi-Frey approach, to appeal to intricate image of inertia arguments.
DOI : 10.4064/aa163-4-3
Keywords: study coprime integer solutions equation using galois representations modular forms represents perhaps natural family generalized fermat equations descended spherical cases which amenable resolution using so called modular method techniques involve elaborate combination ingredients ranging mathbb q curves delicate multi frey approach appeal intricate image inertia arguments

Michael A. Bennett 1 ; Imin Chen 2 ; Sander R. Dahmen 3 ; Soroosh Yazdani 4

1 Department of Mathematics University of British Columbia Vancouver, British Columbia, V6T 1Z2, Canada
2 Department of Mathematics Simon Fraser University Burnaby, British Columbia, Canada
3 Department of Mathematics VU University Amsterdam De Boelelaan 1081a 1081 HV Amsterdam, The Netherlands
4 Department of Mathematics and Computer Science University of Lethbridge Lethbridge, Alberta, T1K 3M4, Canada 
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Michael A. Bennett; Imin Chen; Sander R. Dahmen; Soroosh Yazdani. On the equation $a^{3} + b^{3n} = c^{2}$. Acta Arithmetica, Tome 163 (2014) no. 4, pp. 327-343. doi : 10.4064/aa163-4-3. http://geodesic.mathdoc.fr/articles/10.4064/aa163-4-3/

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