diff --git a/FormalConjectures/OEIS/80170.lean b/FormalConjectures/OEIS/80170.lean index e5e8bd03e1..528d5bd917 100644 --- a/FormalConjectures/OEIS/80170.lean +++ b/FormalConjectures/OEIS/80170.lean @@ -58,8 +58,18 @@ def PrimePowerCondition (k : ℕ) : Prop := /-- Conjecture: The gcd condition is equivalent to the prime power condition. +This has been conjectured by Ralf Stephan. + +Both the natural-language proof and its Lean 4 formalization were carried out +by the KLMM MechMath Agent Team; see the `formal_proof` attribute. + +*References:* +- [Ralf Stephan, *Prove or Disprove. 100 Conjectures from the OEIS*, 2004, Conjecture 17 (arXiv:math/0409509)](https://arxiv.org/abs/math/0409509) +- [Dakai Guo et al., *A Greatest Common Divisor Criterion of Certain Binomial Coefficients*, 2026 (arXiv:2606.22997)](https://arxiv.org/abs/2606.22997) -/ -@[category research open, AMS 11] +@[category research solved, AMS 11, +formal_proof using formal_conjectures at +"https://github.com/guodk/formal-conjectures/blob/0720658844d76a50d48e4baa152eef14d4462907/FormalConjectures/OEIS/80170.lean#L1823"] theorem gcdCondition_iff_primePowerCondition (k : ℕ) (hk : 2 ≤ k) : GCDCondition k ↔ PrimePowerCondition (k + 1) := by sorry diff --git a/FormalConjectures/Subsets/FC100OpenSet1.lean b/FormalConjectures/Subsets/FC100OpenSet1.lean index b89b425500..ffe2a5a39e 100644 --- a/FormalConjectures/Subsets/FC100OpenSet1.lean +++ b/FormalConjectures/Subsets/FC100OpenSet1.lean @@ -221,6 +221,6 @@ end Subsets.FC100OpenSet1 open Lean Meta ProblemAttributes in #eval verifyCategoryCounts Subsets.FC100OpenSet1.problems [ - ("research open", 96), - ("research solved", 4) + ("research open", 95), + ("research solved", 5) ]