## While every ideal in an algebraic integer ring is generated by two elements, an arbitrary generating set need not contain a two-element generating set

Exhibit an ideal $A \subseteq \mathbb{Z}$ such that $A = (a,b,c)$ but $A$ is not equal to any of $(a,b)$, $(a,c)$, and $(b,c)$.

Consider $(6,10,15) = (1)$, and note that $(6,10) = (2)$, $(6,15) = (3)$, and $(10,15) = (5)$.