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Erdős problem 689

Let n be sufficiently large. Is there some choice of congruence class a_p for all primes 2 ≤ p ≤ n such that every integer in [1,n] satisfies at least two of the congruences ≡ a_p (mod p)?

No current result

No reviewed Result is current in Vela Mathematics Program. Retained source material is shown below.

Retained declaration

FormalConjectures/ErdosProblems/689.lean

Formal Conjectures

FormalConjectures/ErdosProblems/689.leanErdos689.erdos_6892 linesExact file
sorry  ∀ᶠ (n : ℕ) in Filter.atTop, ∃ a, ∀ mFinset.Icc 1 n, 2 ≤ {pFinset.Icc 1 n | Nat.Prime pa pm [MOD p]}.card
OpenStatement only, no proof

Reported activity

Work these sources record against this Problem. Source-reported attribution, not reviewed here.

  • AI collaborating with humans

    Erdős AI contributions wiki · 29 Oct, 2025-2 Jun, 2026

    Machine
    Codex, GPT-5.2, GPT-5.5 Pro
    People
    Boris Alexeev, Przemek Chojecki, Dogmachine, jleng01, Mehtaab Sawhney, Terence Tao, Malek Zribi
    Open the source record

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