Integral_Domain_of_Prime_Order_is_Field_v2

Let $\left({\Z_p, +_p, \times_p}\right)$ be the ring of integers modulo $p$. The following statements are equivalent $(1): \quad p$ is a prime. $(2): \quad \left({\Z_p, +_p, \times_p}\right)$ is an integral domain. $(3): \quad \left({\Z_p, +_p, \times_p}\right)$ is a field.