All the Exact Covering Systems with Distinct Moduli Except for the Largest t\
hat is repeated Up to, 32, Times
By Shalosh B. Ekhad
An EXACT covering System is a set of congruences a_i(mod m_i), i=1..k, with\
m_1<=...<=m_k such that every positive integer
belongs to exactly one of these residue classes. A classical theorem of Erd\
os, Davenport, Newman, and Mirsky
asserts that the largest modulus must be repeated at least twice.
We are interested in such systems where all the moduli are distinct, except \
the largest, that is repeated a
specified number of times.
In other words, we have m_1