Past exam of the mathematics course of the University of Cambridge / 2006 / ib / Paper 3 / 1E / ii

Use the standard convention that an integral domain has $1\ne 0$. Since $(n)=(-n)$, the sign of a nonzero $n$ makes no difference. For $|n|=p$ prime, every nonzero residue has an inverse by Bézout's identity, so the quotient ring is a field and hence an integral domain. If $|n|=ab$ is composite with $1<a,b<|n|$, the nonzero classes of $a$ and $b$ multiply to zero, giving zero divisors. For $n=\pm 1$, the quotient is the zero ring, excluded by the convention above. Finally, $n=0$ gives $\mathbb{Z}/(0)\cong \mathbb{Z}$, an integral domain. ThusIf a convention restricts this notation to positive moduli, the answer is simply the positive primes.