Skip to content

Erdős problem 279

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

Sources

Browse retained paths and inspect the exact material available for this Problem.

1 retained statement2415f78e850a

Open selected source

FormalConjectures/ErdosProblems/

279.lean

Retained formal statement1 of 1

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

FormalConjectures/ErdosProblems/279.leanErdos279.erdos_2791 lineExact file
True ↔ ∀ 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

Search problems.science

Find a Problem, Result, source, or page