Problem 278

Erdős Problem #278: declared status 'open'. Formalized: no. Let $A=\{n_1<\cdots<n_r\}$ be a finite set of integers. What is the maximum density of integers covered by a suitable choice of congruences $a_i\pmod{n_i}$? Is the minimum density achieved when all the $a_i$ are equal? Prize: no. Tags: covering systems, number theory.