152.lean`

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

3 declarations, 2 contain sorry, 0 declared as axioms

Erdős Problem 152

#TODO: Formalize the corresponding conjecture for infinite Sidon sets.

References:

erdosproblems.com/152
[DM26a] DeepMind prover agent, formal proof of Erdős problem 152 (2026)
[DM26b] DeepMind prover agent, formal proof of the quadratic variant of Erdős problem 152 (2026)
[ESS94] Erdős, P. and Sárközy, A. and Sós, T., On Sum Sets of Sidon Sets, I. Journal of Number Theory (1994), 329-347.

Imports (1)

FormalConjecturesUtil

def Erdos152.f Define f n to be the minimum of |{s | s - 1 ∉ A + A, s ∈ A + A, s + 1 ∉ A + A}| as A ranges over all Sidon sets of size n line 42 source
Source documentation
Define f n to be the minimum of |{s | s - 1 ∉ A + A, s ∈ A + A, s + 1 ∉ A + A}| as A ranges over all Sidon sets of size n.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Nat
Proof uses: iInf, Set, Set.ofPred, And, Eq, Set.ncard, IsSidon, Not, Membership.mem, HAdd.hAdd, HSub.hSub, OfNat.ofNat
11 instances, coercions and auxiliary constants left out.
```
noncomputable def f (n : ℕ) : ℕ :=
…
```
theorem Erdos152.erdos_152 sorry line 53 source
depends on sorry what this means
Statement uses: Iff, True, Filter.Tendsto, Nat, Erdos152.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.
theorem Erdos152.erdos_152.variants.square sorry line 63 source
depends on sorry what this means
Statement uses: Iff, True, Asymptotics.IsBigO, Nat, Real, Filter.atTop, HPow.hPow, OfNat.ofNat, Erdos152.f
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
18 instances, coercions and auxiliary constants left out.

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