## Sylvester’s problem and mock Heegner points

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- by Samit Dasgupta and John Voight PDF
- Proc. Amer. Math. Soc.
**146**(2018), 3257-3273 Request permission

## 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 $x,y \in \mathbb {Q}$.## References

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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
- MR Author ID: 727424
- ORCID: 0000-0001-7494-8732
- 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
- © Copyright 2018 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**146**(2018), 3257-3273 - MSC (2010): Primary 11D25, 11G05, 11G40, 11G15
- DOI: https://doi.org/10.1090/proc/14008
- MathSciNet review: 3803653