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Number theory

Erdős 357 - infinite set density

Suppose AA is an infinite set such that all finite sums of consecutive terms of AA are distinct. Then it is conjectured that AA has density 0.

Formal statement

Lean type

∀ (A : ℕ → ℕ), StrictMono A → Erdos357.HasDistinctSums A → (Set.range A).HasDensity 0

What you must prove

import FormalConjectures.ErdosProblems.«357»
import TaskSupport

namespace Bounty

theorem target : fcTypeOfName% "Erdos357.erdos_357.variants.infinite_set_density" := by
  sorry

end Bounty

Pinned source: FormalConjectures/ErdosProblems/357.lean

Source type SHA-256
sha256:3c615fd37ffe35e2505e2abad44f7b5b042c5625563adb5fda0e60f4caec8364
Task id
fc-379fc029-variants-infinite-set-density-20987dfd50-formalized-v1
Task commitment
sha256:674ddbfd8885dcdf5d07dbb8b39573165a2e6836791024d6c34d3a9041cdab5e

Something wrong with this formalization?

A statement that does not faithfully capture the original conjecture is the one real risk here, so we would rather hear about it early - before someone spends weeks on it.