 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2025/ib/paper-2/9e/a/solution

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

For a nonzero ideal

I

, choose

a \in I

of minimal Euclidean value. Divide any

x \in I

a

x = q a + r

. Then

r \in I

, and minimality forces

r = 0

. Hence

I = (a)

; the zero ideal is also principal.

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