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ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2018/ii/paper-2/20g/a/solution

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Past exam of the mathematics course of the University of Cambridge / 2018 / ii / Paper 2 / 20G / a / Solution by

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

The cyclotomic polynomial of the primitive

p

ω

is

Φ_{p} (X) = 1 + X + \dots + X^{p - 1} .

By the irreducibility of cyclotomic polynomials, this is the minimal polynomial of

ω

over

Q

. The prime cyclotomic field degree therefore gives

[L : Q] = de g Φ_{p} = p - 1.

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