Rogers’ theorem on sieving

A basic problem in sieve theory is to understand what happens when we start with the integers (or some subinterval of the integers) and remove some congruence classes for various moduli . Here we shall concern ourselves with the simple setting where we are sieving the entire integers rather than an interval, and are only removing a finite number of congruence classes . In this case, the set of integers that remain after the sieving is periodic with period , so one work without loss of generality...