You&#x27;re right in that evenness is divisibility by two by definition. For any P which is prime, P is the smallest divisible by P.<p>It is probably that divisibility by two (evenness) is interesting.<p>For example, it has the property that if we know the evenness of two integers, then we know the evenness of their sum or product.<p>Division of cases by even versus odd occurs regularly; in few circumstances do you have to separately reason about cases corresponding somehow to the elements of the congruence modulo 37.