4.I .2E. 2 \mathrm{E} \quad

Groups, Rings and Modules
Part IB, 2006

How many elements does the ring Z[X]/(3,X2+X+1)\mathbb{Z}[X] /\left(3, X^{2}+X+1\right) have?

Is this ring an integral domain?

Briefly justify your answers.