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updated open to formally solved for 434 lean #3590

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updated open to formally solved for 434 lean #3590

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updated open to formally solved for 434 lean
aryanamol10 Mar 17, 2026
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Merge branch 'main' into statusmismatch
aryanamol10 Mar 17, 2026
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4 changes: 2 additions & 2 deletions FormalConjectures/ErdosProblems/434.lean
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Expand Up @@ -47,7 +47,7 @@ maximises the number of integers not representable as the sum of finitely
many elements from $A$ (with repetitions allowed)?
Is it $\{n, n - 1, \dots, n - k + 1\}$?
-/
@[category research open, AMS 11]
@[category research formally solved, AMS 11]
theorem erdos_434.parts.i (n k : ℕ) (hn : 1 ≤ n) (hk : 1 ≤ k) (h : k ≤ n) :
IsGreatest
{ Nat.NcardUnrepresentable S | (S : Finset ℕ) (_ : S ⊆ Finset.Icc 1 n)
Expand All @@ -60,7 +60,7 @@ Let $k \le n$. Out of all $A\subseteq\{1, \dots, n\}$ (with $\text{gcd}(A) = 1$)
does $A = \{n, n - 1, \dots, n - k + 1\}$ maximise the number of integers
not representable as the sum of finitely many elements from $A$ (with repetitions allowed)?
-/
@[category research open, AMS 11]
@[category research formally solved, AMS 11]
theorem erdos_434.parts.ii : answer(sorry) ↔ ∀ᵉ (n ≥ 1) (k ≥ 1), k ≤ n →
IsGreatest
{ Nat.NcardUnrepresentable S | (S : Finset ℕ) (_ : S ⊆ Finset.Icc 1 n)
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