 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2022/ii/paper-1/20h/c/iii/solution

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

Take

K = Q (i)

and

α = \frac{3 + 4 i}{5} .

Its two embeddings give

(3 \pm 4 i) /5

, both of modulus one. But

a lp ha \in / Z [i] = O_{K}

, since its real and imaginary parts are not integers. This is the required example.

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