Solution
= Solution
In $R=\mathbb Z[\sqrt5]$, take $I=J_1=(2,1+\sqrt5)$ and $J_2=(2)$. Direct multiplication gives $I^2=(4,2+2\sqrt5,6+2\sqrt5)=2I=IJ_2$, but $I\ne(2)$.
= Solution
In $R=\mathbb Z[\sqrt5]$, take $I=J_1=(2,1+\sqrt5)$ and $J_2=(2)$. Direct multiplication gives $I^2=(4,2+2\sqrt5,6+2\sqrt5)=2I=IJ_2$, but $I\ne(2)$.