On the shortest open cubic equations
General Mathematics
2026-05-18 v2
Abstract
We use cubic reciprocity to prove that the equation 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.
Cite
@article{arxiv.2603.29831,
title = {On the shortest open cubic equations},
author = {Bogdan Grechuk and Ashleigh Ratcliffe},
journal= {arXiv preprint arXiv:2603.29831},
year = {2026}
}
Comments
Accepted to International Journal of Number Theory