Every ideal $I \trianglelefteq \mathbb{Z}$ is principal. More precisely, for every ideal $I \trianglelefteq \mathbb{Z}$, there exists a unique integer $d \ge 0$ such that
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\begin{align*}
I = (d) = d\mathbb{Z} = \{dn : n \in \mathbb{Z}\}.
\end{align*}