246.lean`

Explanation legend Lean4 Domain Explanation Language (L4DEL)

L4DEL explanations are a separate layer. They do not change the Lean source. Intuition is explanatory prose; numbered items are a reading path; sources link the wording back to evidence.

L4DEL: Lean4 Domain Explanation Language

Annotation provenance. This overlay contains 10 curated AI-written annotations and 7190 mechanical source-derived annotations. They have not been human-reviewed as explanations; treat them as unverified and not mathematical authority. Retained generation history: The 71 original curated annotations were produced in a Claude Sonnet 5.5 session at medium effort; Claude Opus 5.5 is recorded in that session as the advisor model, not the direct author. The bulk source-derived expansion was generated mechanically from pinned source comments by tooling developed in a GPT-5.6 Sol session at ultra reasoning; GPT-5.6 Sol did not originate the quoted source prose. On 2026-10-17 the mechanically generated source-comment annotations of the Formal Conjectures, Carleson, FLT, PFR, CompFiles, Mathematics in Lean and Theorem Proving in Lean overlays were regenerated by the same generator after three corrections made in a Claude Sonnet 5.5 session: titles no longer cut a sentence inside mathematics or end on a dangling word, workflow markers are removed from the quoted prose, and declaration names follow the scanner's namespace resolution. The boilerplate step line was dropped, and comments that were only a row of dashes no longer yield annotations. No new prose was written and no human review is claimed.

Credit: The upstream authors and contributors retain credit for the project and mathematics. lean4-explainer only renders their pinned source and adds the separately disclosed explanation layer.

Project sources: Pinned project documentation, Formal Conjectures paper, arXiv v1

2 declarations, 1 contain sorry, 0 declared as axioms

Erdős Problem 246

References:

erdosproblems.com/246
[Bi59] Birch, B. J., Note on a problem of Erd\H{o}s. Proc. Cambridge Philos. Soc. (1959), 370-373.
[Ca60] Cassels, J. W. S., On the representation of integers as the sums of distinct summands taken from a fixed set. Acta Sci. Math. (Szeged) (1960), 111-124.
[FaCh17] Fang, Jin-Hui and Chen, Yong-Gao, A quantitative form of the {E}rd\H{o}s-{B}irch theorem. Acta Arith. (2017), 301--311.
[He00b] Hegyv'{a}ri, N., On the completeness of an exponential type sequence. Acta Math. Hungar. (2000), 127--135.
[Yu24] Yu, Wang-Xing, On the representation of an exponential type sequence. Publ. Math. Debrecen (2024), 253--261.

Imports (1)

FormalConjecturesUtil

Imported by 1 file

FormalConjectures/ErdosProblems/1110.lean

def Erdos246.Gamma The set $\{a^k b^l : k,l \geq 0\}$ line 43 source
Source documentation
The set $\{a^k b^l : k,l \geq 0\}$.

standard axioms: propext what this means
Statement uses: Nat, Set
Proof uses: Set.ofPred, Exists, Eq, HMul.hMul, HPow.hPow
6 instances, coercions and auxiliary constants left out.
```
def Gamma (a b : ℕ) : Set ℕ :=
…
```
theorem Erdos246.erdos_246 sorry line 53 source
depends on sorry what this means
Statement uses: Nat, LE.le, OfNat.ofNat, Nat.Coprime, IsAddComplete, Erdos246.Gamma
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
8 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.