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← Erdős 26 — thick sequences and Behrend density
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Lean 4.29.1
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Mathlib v4.29.1
Ubuntu 24.04 LTS · x86_64 · toolchain via elan
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12 days ago
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Lean 4 / Mathlib
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import Mathlib /-- Let $A\subset\mathbb{N}$ be infinite such that $\sum_{a \in A} \frac{1}{a} = \infty$. Must there exist some $k\geq 1$ such that almost all integers have a divisor of the form $a+k$ for some $a\in A$? This was formalized in Lean by Alexeev using Aristotle. -/ @[category research solved, AMS 11, formal_proof using lean4 at "https://github.com/plby/lean-proofs/blob/main/src/v4.24.0/ErdosProblems/Erdos26.lean"] theorem erdos_26 : answer(False) ↔ ∀ A : ℕ → ℕ, StrictMono A → IsThick A → ∃ k, IsBehrend (A · + k) := by sorry
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