Erdős Problem #279 — Let k≥ 3. Is there a choice of congruence classes a_p pmodp for every prime p such that all sufficiently large integers can be written as a_p+tp for some prime p and integer t≥ k?

Question

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

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 $t\geq k$ ?

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