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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)?

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1 retained statement2415f78e850a

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FormalConjectures/ErdosProblems/

689.lean

Retained formal statement1 of 1

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)?

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

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