 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2023/ii/paper-3/10d/c/solution

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

33

1 0^{2} = 100 \equiv 1, 10 \neq \equiv 1,

ord_{33} (10) = 2

. This order is even and

1 0^{2/2} = 10 \neq \equiv - 1 (mod 33) .

g cd (10 - 1, 33) = 3, g cd (10 + 1, 33) = 11.

Thus

33 = 3 \cdot 11.

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