I have to prove that $\mathbb Z [X] / (X) \cong \mathbb Z[X] / (X+1) \cong \mathbb Z [X] / (X+2015)$.
I think that one answer could be that $\mathbb Z[X]/(X) \cong \mathbb Z(0)$, $\mathbb Z[X]/(X+1)\cong Z(-1)$ and $\mathbb Z [X] /(X+2015)\cong \mathbb Z(-2015)$, as $0, -1, -2015$ are roots of these polynomials. Also, as $0, -1, -2015\in \mathbb Z$, then all of them are isomorphic to $\mathbb Z $, hence isomorphic between them.
But I don't know very well how to justify this rigorously and my teacher has said to me that there is a simpler way to proof this, without using the roots of these polynomials.