 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2025/ii/paper-4/20g/c/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

H = {x \in R^{r + s} : \sum_{j = 1}^{r + s} x_{j} = 0} .

For a fundamental system

u_{1}, \dots, u_{m}

, where

m = r + s - 1

Log (u_{1}), \dots, Log (u_{m})

are linearly independent, form a real basis of

H

, and generate the full lattice

Log (O_{K}^{\times}) = ⨁_{i = 1}^{m} Z Log (u_{i}) .

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