Covering system

In mathematics, a covering system (also called a complete residue system) is a collection

${\displaystyle \{a_{1}{\pmod {n_{1}}},\ \ldots ,\ a_{k}{\pmod {n_{k}}}\}}$

of finitely many residue classes

${\displaystyle a_{i}{\pmod {n_{i}}}=\{a_{i}+n_{i}x:\ x\in \mathbb {Z} \},}$

whose union contains every integer.