Abstract
We show that the equation has no nontrivial positive integer solutions with via a combination of techniques based upon the modularity of Galois representations attached to certain -curves, corresponding surjectivity results of Ellenberg for these representations, and extensions of multi-Frey curve arguments of Siksek.
Citation
Michael A. Bennett. Imin Chen. "Multi-Frey $\mathbb{Q}$-curves and the Diophantine equation $a^2+b^6=c^n$." Algebra Number Theory 6 (4) 707 - 730, 2012. https://doi.org/10.2140/ant.2012.6.707
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