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Register a new userOn the generalized Fermat equation $a^2+3b^6=c^n$
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Authors
Angelos Koutsianas
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In this paper, we prove that the only primitive solutions of the equation $a^2+3b^6=c^n$ for $ngeq 3$ are $(a,b,c,n)=(pm 47,pm 2,pm 7,4)$. Our proof is based on the modularity of Galois representations of $mathbb Q$-curves and the work of Ellenberg for big values of $n$ and a variety of techniques for small $n$.
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