The board / number theory / #1102
Erdős Problem #1102
SOLVED LEANdatabase updated 2026-02-23
Resolved in some way other than a straight proof or disproof — usual for open-ended questions, or for multi-part problems whose parts went different ways. A solution has also been checked by machine, in Lean.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
Property P : A set \(A ⊆ ℕ \) has property P, if for all \(n ≥ 1\) the set \( \{a ∈ A | n + a\text{ is squarefree}\}\) is finite.
Property Q : A set \(A ⊆ ℕ \) has property Q, if the set \(\{n ∈ ℕ | ∀ a ∈ A, n > a\text{ implies }n + a\text{ is squarefree}\}\) is infinite.
If `A = {a₁ < a₂ < …}` has property P, then `A` has natural density `0`. Equivalently, `(a_j / j) → ∞` as `j → ∞`. -
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research solved · 3 further variants / known partial results in the Lean file. The authoritative wording is on erdosproblems.com/1102.Prizenone
Topicsnumber theory
Statement in LeanFormal Conjectures
Solution in Leanyes
Original pageerdosproblems.com/1102
Attempts
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