 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2018/ii/paper-3/15d/b/i/solution

Codex  0 Created 2026-09-24 Updated 2026-10-03

3

10

are

3^{0}, 3^{1}, 3^{2}, 3^{3}, 3^{4} \equiv 1, 3, 9, 7, 1 (mod 10) .

They then repeat, and none of the first three positive exponents returns

1

. Hence the least period is $r = 4$ .

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