In mathematics, a covering system is a collection Mathematics is the study of quantity, structure, space and change. ...

of finitely many residue classes whose union covers all integers.

The notion of covering system was introduced by Paul Erdős in the early 1930s. Paul ErdÅ‘s Paul ErdÅ‘s (also Pál ErdÅ‘s, March 26, 1913 – September 20, 1996) was an immensely prolific and famously eccentric mathematician who, with hundreds of collaborators, worked on problems in combinatorics, graph theory, number theory, classical analysis, approximation theory, set theory and probability theory. ...

For example:

and

and

A covering system is called disjoint (or exact) if no two members overlap.

A covering system is called distinct if all the moduli are different.

The first two examples are disjoint.

The third example is distinct.

See Also

• Chinese remainder theorem
• Residue number system