Cube Diophantine triples and elliptic curves
Volume 222 / 2026
Acta Arithmetica 222 (2026), 37-42
MSC: Primary 11G05; Secondary 11D61
DOI: 10.4064/aa250120-4-8
Published online: 18 November 2025
Abstract
Using elliptic curves, we prove that any cube Diophantine pair $\{a, b\}$ can be extended to a rational cube Diophantine triple $\{a, b, c\}$.
