Example of ideal generated by two elements I have an easy example on my notes that I don't understand. My teacher said that in $\mathbb{Z}$, $(2,3)=2\mathbb{Z}+3\mathbb{Z}$ is a principal ideal, because $2\mathbb{Z}+3\mathbb{Z}=\mathbb{Z}$. How she could say that without proving it? What am I overlooking? Thanks in advance.

We have $3+-2=1 \in (3,2)$, hence the generated ideal contains $1$, hence it contains $\mathbb Z$
