Midy’s theorem on repeating decimals
Theorem.Midy’s theorem on repeating decimals — for prime p∉{2,5} with 1/p of even period 2k, the two halves of the repetend sum to 10^k−1 (142+857=999).
Proof.for prime p∉{2,5} with 1/p of even period 2k, the two halves of the repetend sum to 10^k−1 (142+857=999) — verified in exact BigInt for every applicable p ≤ 100, riding ord_p(10) as the period.
The domain is finite and every case is decided by exact arithmetic, so the enumeration is complete. ∎
src/4/6/index.ts#discoveredTheoremsWaveFiftySeven
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
"Midy’s theorem on repeating decimals" 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 discoveredTheoremsWaveFiftySeven.
- 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 (discoveredTheoremsWaveFiftySeven @ 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 discoveredTheoremsWaveFiftySeven (src/4/6/index.ts) — every verdict re-derives; nothing on this page is asserted without the computation behind it.