 Solution

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

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

Let

a

and

b

generate

C_{m}

and

C_{n}

. The order of

(a, b)

lcm (m, n) .

When

g cd (m, n) = 1

, this is

mn = ∣ C_{m} \times C_{n} ∣

. Hence

(a, b)

generates the whole product and

C_{m} \times C_{n} ≅ C_{mn} .

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