Back to Problems

erdos_332

Specification

Let $A\subseteq \mathbb{N}$ and $D(A)$ be the set of those numbers which occur infinitely often as $a_1 - a_2$ with $a_1, a_2\in A$. What conditions on $A$ are sufficient to ensure $D(A)$ has bounded gaps? This is formalised here using the `answer(sorry)` mechanism. In order to solve this problem one has to provide what the sufficient conditions are, and proof that they imply the desired condition. If the condition is a solution to the problem is up to human judgement.

Actions

Submit a Proof

Have a proof attempt? Submit it for zero-trust verification.

Submit Proof
Lean 4 Statement
theorem erdos_332 (A : Set ℕ) : (answer(sorry) : Set ℕ → Prop) A → HasBoundedGaps (D_A A)
ID: ErdosProblems__332__erdos_332
Browse 300 unsolved math conjectures formalized in Lean 4
Browse

All Problems

Explore all 300 unsolved conjectures.

View problems →
ASI Prize documentation for formal verification pipeline
Docs

Verification Pipeline

How zero-trust verification works.

Read docs →
Evaluation Results

Recent Submissions

No submissions yet. Be the first to attempt this problem.