Congruent Number

formal-conjectures · wikipedia · ams-11

A natural number $n$ is called a congruent number if there exists a right triangle with rational
sides $a$, $b$, and hypotenuse $c$ such that the area of the triangle is $\frac{1}{2}ab = n$.

Tunnell's theorem (sufficient condition assuming BSD) for odd squarefree congruent numbers.

Mathematical status
Open: marked research open in google-deepmind/formal-conjectures at revision cd3d8db4634733a748b2380f80f77ba3e4b9dda0 (checked 2026-09-11).

Formal availability
A Prop definition is supplied for the pinned Lean 4.33.1 environment and must be accepted by the deployed verifier before it is available.

Sources and provenance
Upstream reference cited by formal-conjectures (checked 2026-09-11): https://en.wikipedia.org/wiki/Congruent_number
Upstream reference cited by formal-conjectures (checked 2026-09-11): https://en.wikipedia.org/wiki/Tunnell%27s_theorem
Upstream reference cited by formal-conjectures (checked 2026-09-11): https://kconrad.math.uconn.edu/blurbs/ugradnumthy/congnumber.pdf
Formal statement provenance (Apache-2.0) (checked 2026-09-11): https://github.com/google-deepmind/formal-conjectures/blob/cd3d8db4634733a748b2380f80f77ba3e4b9dda0/FormalConjectures/Wikipedia/CongruentNumber.lean
Local target: Corpus.WikipediaCongruentNumber.Tunnell_odd_converse
Source SHA-256: 193583e2b47dff6b56d210ffc197622f7ed31f69927d2d1f248201341b9bc9eb
Lean v4.33.1; Mathlib 0df444a360eaa60ab8c11dca51a86af692955474; policy kernel-replay-v1.
The deployed accepted environment records the actual immutable verifier image.

Research discussions are not verified proofs. A formal target specifies a precise statement; accepting a target does not prove it. Checked results apply to their exact statements and pinned environments.

Public JSON record