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updated mismatch to "solved" from open mismatch at lean 868 #3591

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updated mismatch to "solved" from open mismatch at lean 868 #3591

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5840861
updated mismatch to "solved" from open
aryanamol10 Mar 17, 2026
0c85657
Merge branch 'main' into mismatch868
aryanamol10 Mar 17, 2026
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4 changes: 2 additions & 2 deletions FormalConjectures/ErdosProblems/868.lean
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Expand Up @@ -37,7 +37,7 @@ def ncard_add_repr (A : Set ℕ) (o : ℕ) (n : ℕ) : ℕ :=
/-- Let $A$ be an additive basis of order $2$, let $f(n)$ denote the number of ways in which
$n$ can be written as the sum of two elements from $A$. If $f(n) \to \infty$ as $n \to \infty$, then
must $A$ contain a minimal additive basis of order $2$? -/
@[category research open, AMS 5 11]
@[category research solved, AMS 5 11]
theorem erdos_868.parts.i :
answer(sorry) ↔ ∀ (A : Set ℕ), A.IsAsymptoticAddBasisOfOrder 2 →
atTop.Tendsto (fun n => ncard_add_repr A 2 n) atTop → ∃ B ⊆ A,
Expand All @@ -48,7 +48,7 @@ theorem erdos_868.parts.i :
$n$ can be written as the sum of two elements from $A$. If $f(n) > \epsilon \log n$ for large $n$
and an arbitrary fixed $\epsilon > 0$, then must $A$ contain a minimal additive
basis of order $2$? -/
@[category research open, AMS 5 11]
@[category research solved, AMS 5 11]
theorem erdos_868.parts.ii :
answer(sorry) ↔ ∀ᵉ (A : Set ℕ) (ε > 0), A.IsAsymptoticAddBasisOfOrder 2 →
(∀ᶠ (n : ℕ) in atTop, ε * Real.log n < ncard_add_repr A 2 n) → ∃ B ⊆ A,
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