485.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 485

References:

erdosproblems.com/485
[Re47] Rényi, A., On the minimal number of terms of the square of a polynomial. Hungarica Acta Math. (1947), 30-34.
[Er49b] Erdős, P., On the number of terms of the square of a polynomial. Nieuw Arch. Wiskunde (2) (1949), 63-65.
[Er61] Erdős, Paul, Some unsolved problems. Magyar Tud. Akad. Mat. Kutató Int. Közl. (1961), 221-254.
[Ha74] Hayman, W. K., Research problems in function theory: new problems. (1974), 155--180.
[Sc87] Schinzel, A., On the number of terms of a power of a polynomial. Acta Arith. (1987), 55-70.
[ScZa09] Schinzel, Andrzej and Zannier, Umberto, On the number of terms of a power of a polynomial. Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. (2009), 95-98.

Imports (1)

FormalConjecturesUtil

def Erdos485.f The minimum number of terms of the square of a rational polynomial with exactly k nonzero terms, where the number of terms of P is P.support.card line 47 source
Source documentation
The minimum number of terms of the square of a rational polynomial with exactly k nonzero terms, where the number of terms of P is P.support.card.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Nat
Proof uses: InfSet.sInf, Set.ofPred, Exists, Polynomial, Rat, And, Eq, Finset.card, Polynomial.support, HPow.hPow, OfNat.ofNat
8 instances, coercions and auxiliary constants left out.
```
noncomputable def f (k : ℕ) : ℕ :=
…
```
theorem Erdos485.erdos_485 sorry line 62 source
depends on sorry what this means
Statement uses: Iff, True, Filter.Tendsto, Nat, Erdos485.f, Filter.atTop
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous, OfNat.ofNat
3 instances, coercions and auxiliary constants left out.

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