Covering system
In mathematics, a covering system (also called a complete residue system) is a collection { a 1 ( mod n 1 ) , … , a k ( mod n k ) } {\displaystyle \{a_{1}{\pmod {n_{1}}},\ \ldots ,\ a_{k}{\pmod {n_{k}}}\}} of finitely many residue classes a i ( mod n i ) = { a i + n i x : x ∈ Z } , {\displaystyle a_{i}{\pmod {n_{i}}}=\{a_{i}+n_{i}x:\ x\in \mathbb {Z} \},} whose union contains every integer. == Examples and definitions == The notion of covering system was introduced by Paul Erdős in the early 1930s.