 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2025/ii/paper-4/1g/c/i/solution

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

The class

X = - 1

satisfies

X^{3} = - 1

for every prime. Thus a solution exists for every odd prime

p

, regardless of its residue class modulo

3

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