Exact Covering System

A system of congruences $a_i$ mod $n_i$ with $1\leq i\leq k$ is called a Covering System if every Integer $y$ satisfies $y\equiv a_i\ \left({{\rm mod\ } {n}}\right)$ for at least one value of $i$. A covering system in which each integer is covered by just one congruence is called an exact covering system.

See also Covering System

References

Guy, R. K. ``Exact Covering Systems.'' §F14 in Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, pp. 253-256, 1994.