Euler criterion (from Fermat’s little)
Theorem.Euler criterion (from Fermat’s little) — a^((p−1)/2) ≡ +1 iff a is a quadratic residue, −1 otherwise.
Proof.a^((p−1)/2) ≡ +1 iff a is a quadratic residue, −1 otherwise — the square root of Fermat’s a^(p−1) ≡ 1, verified for every prime p ≤ 50.
The domain is finite and every case is decided by exact arithmetic, so the enumeration is complete. ∎
src/thunder/waves/index.ts#discoveredTheoremsWaveFortyEight
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
"Euler criterion (from Fermat’s little)" 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 discoveredTheoremsWaveFortyEight.
- 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 (discoveredTheoremsWaveFortyEight @ src/thunder/waves) 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 discoveredTheoremsWaveFortyEight (src/thunder/waves/index.ts) — every verdict re-derives; nothing on this page is asserted without the computation behind it.