The modulus condition over the rational integers is ordinary congruence

Under $\mathcal O_{\mathbb Q}\simeq\mathbb Z$, the condition that $a-1$ belongs to the ideal generated by $n$ is exactly the congruence $a\equiv1\pmod n$. The statement uses an explicit integer witness $a=1+nk$ and holds also at $n=0$, where it reduces to $a=1$. Along with positivity at the unique real place, this is the local algebra needed to identify the narrow ray condition for $\mathbb Q$ with a positive integer congruence.