Erdős problem 279

Let $k\geq 3$ . Is there a choice of congruence classes $a_p\pmod{p}$ for every prime $p$ such that all sufficiently large integers can be written as $a_p+tp$ for some prime $p$ and integer $t\geq k$ ?

Sources

The source's own material, retained exactly.

1 retained statement36c6d0fef71a

FormalConjectures/ErdosProblems/

279.lean

Retained formal statement1 of 1

Let $k\geq 3$ . Is there a choice of congruence classes $a_p\pmod{p}$ for every prime $p$ such that all sufficiently large integers can be written as $a_p+tp$ for some prime $p$ and integer $t\geq k$ ?

FormalConjectures/ErdosProblems/279.leanErdos279.erdos_2791 lineExact file

1True ↔ ∀ k ≥ 3, ∃ a N, (∀ (p : ℕ), Nat.Prime p → a p < p) ∧ ∀ n ≥ N, ∃ p, ∃ t ≥ k, Nat.Prime p ∧ n = a p + t * p

OpenStatement only, no proof