To put it another way, Zp consists of the remainders {0,1,...,p-1}, so that p=0. For instance, Z3 has the following addition and multiplication tables:
| + 0 1 2 | 0 0 1 2 | 1 1 2 0 | 2 2 0 1
| * 0 1 2 | 0 0 0 0 | 0 0 1 2 | 0 0 2 1
When p is a composite number, the factors of p are going to turn out to be ZeroDivisors?. When p is prime, these don't exist, and so Zp is an IntegralDomain? and in fact necessarily a field.