Write $m=\prod_pp^{n_p}$. For the modulus $m\infty$,
$$
\mathbb I_{\mathbb Q}(m\infty)
=\mathbb R_{>0}\times
\prod_{p\mid m}(1+p^{n_p}\mathbb Z_p)
\times\prod_{p\nmid m}\mathbb Z_p^\times.
$$
This is understood as the corresponding restricted-product subgroup of $\mathbb I_{\mathbb Q}$.


Solution

Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 123 / 4 / c / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2024/iii/paper-123/4/c/solution