If solved
Rational Solutions Predictable
For any elliptic curve one can compute from its L-function whether and how many rational solutions exist, with proof.
Open in the interactive tree →A proof would turn decades of numerical evidence into a theorem and settle long-open questions about which numbers are areas of right triangles with rational sides. It would also give exact control over the hidden Tate-Shafarevich group.
What it brings
- A complete answer to the congruent number problem
- Provable rank computation from L-function data
- Exact sizes of Tate-Shafarevich groups