 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2021/ia/paper-3/5d/d/i/solution

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

Write

d = q r + s

with

0 \leq s < r

. Since

x^{d} = e \in H

and

x^{r} \in H

x^{s} = x^{d} (x^{r})^{- q} \in H .

The minimality of the positive integer

r

s = 0

. Therefore

r ∣ d .

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