 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2022/ii/paper-3/11i/c/solution

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

25

. The positive integers below eight either fail to be units or have orders

ord_{25} (1) = 1, ord_{25} (4) = 10, ord_{25} (6) = 5, ord_{25} (7) = 4,

whereas

ord_{25} (2) = ord_{25} (3) = ord_{25} (8) = 20.

Therefore the three smallest required integers are

2, 3, 8 .

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