Problem 689

Erdős Problem #689: declared status 'open'. Formalized: yes. Let $n$ be sufficiently large. Is there some choice of congruence class $a_p$ for all primes $2\leq p\leq n$ such that every integer in $[1,n]$ satisfies at least two of the congruences $\equiv a_p\pmod{p}$? Prize: no. Tags: number theory.