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declared disproved (Lean) · formalizederdos:26
Let A⊂NA\subset\mathbb{N} be infinite. Must there exist some k≥1k\geq 1 such that almost all integers have a divisor of the form a+ka+k for some a∈Aa\in A? The question as posed follows negatively from Davenport–Erdős (1951). The AI result settles Tenenbaum's harder variant, also negatively: there is an infinite AA such that for every k≥1k\geq 1 the set of multiples of A+kA+k has upper density below 0.340.34.
number theorydivisorsN/A6 sources
declared disproved (Lean) · formalizederdos:692
False ↔ ∀ (δ : ℕ → ℕ → ℝ), (∀ (a b : ℕ), Erdos692.IsDelta₁ a b (δ a b)) → ∀ (n : ℕ), UnimodularOn (δ n) (n + 1)
number theorydivisorsN/A5 sources
declared disproved (Lean) · formalizederdos:884
False ↔ Erdos884.Erdos884Prop
number theorydivisorsN/A3 sources

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