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declared falsifiable · formalized · $100erdos:97
True ↔ ∀ (A : Finset (EuclideanSpace ℝ (Fin 2))), A.Nonempty → EuclideanGeometry.ConvexIndep ↑A → ¬Erdos97.HasNEquidistantProperty 4 A
geometrydistancesconvexN/A2 sources
declared falsifiableerdos:106
If f(n)f(n) is the maximum total side length of nn interior-disjoint squares packed in the unit square, is f(k2+1)=kf(k^2 + 1) = k? An exact rational configuration packs 1717 squares with total side length greater than 44, refuting the identity at k=4k = 4.
geometryN/A3 sources
declared falsifiable · formalized · $500erdos:107
sorry ↔ ∀ n ≥ 3, Erdos107.f n = 2 ^ (n - 2) + 1
geometryconvexA0000512 sources
declared falsifiable · formalizederdos:982
∀ (n : ℕ), 3 ≤ n → ∀ (p : Fin n → EuclideanSpace ℝ (Fin 2)), Function.Injective p → EuclideanGeometry.IsConvexPolygon p → ∃ i, {d | ∃ j, j ≠ i ∧ d = dist (p i) (p j)}.ncard ≥ n / 2
geometryconvexdistancesA0045262 sources
declared falsifiable · formalizederdos:1082
True ↔ ∀ (A : Finset (EuclideanSpace ℝ (Fin 2))), EuclideanGeometry.NonTrilinear ↑A → A.card / 2 ≤ EuclideanGeometry.distinctDistances A
geometrydistancespossible3 sources

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