On the shortest open cubic equations
We use cubic reciprocity to prove that the equation [Formula: see text] has no integer solutions. Prior to this work, it was the shortest cubic equation for which the existence of integer solutions remained open. We conclude with a list of the new shortest open cubic equations.
Authors
- Bogdan Grechuk (ORCID: https://orcid.org/0000-0002-2624-5765)
- Ashleigh Ratcliffe
Publication Details
- Journal
- International Journal of Number Theory
- Published
- 2026-05-22
- DOI
- https://doi.org/10.1142/s1793042126501058
- Primary Topic
- History and Theory of Mathematics
- Type
- article
- Field-Weighted Citation Impact
- 0.00