In mathematics, a covering system is a collection { a 1, …, a k } {\displaystyle \{a_{1}{\pmod {n_{1}}},\ \ldots,\ a_{k}{\pmod {n_{k}}}\}} of finitely many residue classes a 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. Wikipedia