Erdős problem 12 · problems.science

Let $A \subset \mathbb{N}$ be infinite with no distinct $a, b, c \in A$ such that $a \mid (b + c)$ with $b, c > a$ . Can $|A \cap [1, N]|/\sqrt{N}$ have positive lower limit? Must every such $A$ fall below $N^{1-c}$ infinitely often?

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10 retained statements2415f78e850a

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FormalConjectures/ErdosProblems/

12.lean

Retained formal statement9 of 9

The set of $p ^ 2$ where $p \cong 3 \mod 4$ is prime is an example of a good set. Formal proof provided by AlphaProof

FormalConjectures/ErdosProblems/12.leanErdos12.isGood_example1 lineExact file

1Erdos12.IsGood {x | ∃ p, ∃ (_ : p ≡ 3 [MOD 4]) (_ : Nat.Prime p), p ^ 2 = x}

TextbookProof has a holeformal conjecturesexternal proof

The proof uses `sorry`: part of the argument is written but not proved. Lean accepts the file; it does not accept the theorem.

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