Pell’s equation x²−Dy²=1 is solvable
Theorem.Pell’s equation x²−Dy²=1 is solvable — x² − Dy² = 1 has a nontrivial integer solution for every non-square D.
Proof.every non-square D has a nontrivial Pell solution from the CF convergent at the end of √D’s period — verified in exact BigInt for every non-square D ≤ 40.
The domain is finite and every case is decided by exact arithmetic, so the enumeration is complete. ∎
src/4/6/index.ts#discoveredTheoremsWaveSixty
1 · Classification
finite-complete — self-contained computation, no external lean
2 · Provenance
Documented theorem re-derived by exhaustive computation (humanityNovel=false); first-in-this-registry is the only sense of discovered.
Acknowledgment
"Pell’s equation x²−Dy²=1 is solvable" is a re-derivation, acknowledged to documented mathematics — the original proof is the prior art this re-derivation acknowledges; not new to humanity — the contribution is the reproducible computation discoveredTheoremsWaveSixty.
- Prior art
- documented mathematics — the original proof is the prior art this re-derivation acknowledges
- Novelty
- not new to humanity — a re-derivation (humanityNovel = false)
- Contribution
- a reproducible computation (discoveredTheoremsWaveSixty @ src/4/6) that re-derives the result at zero tokens — the contribution is the verifiable recomputation, NOT the theorem
3 · Reproducibility
Recompute from source: npm run theorems:verify recomputes discoveredTheoremsWaveSixty (src/4/6/index.ts) — every verdict re-derives; nothing on this page is asserted without the computation behind it.