Abstract Blankits and Covers Finding Covers with a Large Lowest Modulus

In this paper we will look at different ways to find covers with a large lowest modulus. We found some conditions neccessary for a collection of congruence classes to cover the integers. We determined that certain types of collections of congruence classes cannot cover the integers. To compute a cover we created a program that uses a greedy algorthm to create potential covers by covering the most remaining numbers with each congruence class choosen. In the end, we have a cover with lowest modulus 14