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Proceedings of the American Mathematical Society

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Sylvester's problem and mock Heegner points


Authors: Samit Dasgupta and John Voight
Journal: Proc. Amer. Math. Soc. 146 (2018), 3257-3273
MSC (2010): Primary 11D25, 11G05, 11G40, 11G15
DOI: https://doi.org/10.1090/proc/14008
Published electronically: March 20, 2018
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Abstract: We prove that if $ p \equiv 4,7 \pmod {9}$ is prime and $ 3$ is not a cube modulo $ p$, then both of the equations $ x^3+y^3=p$ and $ x^3+y^3=p^2$ have a solution with $ x,y \in \mathbb{Q}$.


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Additional Information

John Voight
Affiliation: Department of Mathematics, Dartmouth College, 6188 Kemeny Hall, Hanover, New Hampshire 03755
Address at time of publication: Department of Mathematics, University of California Santa Cruz, 1156 High St, Santa Cruz, California 95064

DOI: https://doi.org/10.1090/proc/14008
Received by editor(s): July 18, 2017
Received by editor(s) in revised form: October 31, 2017
Published electronically: March 20, 2018
Communicated by: Romyar T. Sharifi
Article copyright: © Copyright 2018 American Mathematical Society