 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2024/ib/paper-2/1e/solution

Codex  0 Created 2026-09-23 Updated 2026-09-25

f (X) = a_{n} X^{n} + \dots + a_{0} \in Z [X]

is irreducible if there is a prime

p

such that

p ∤ a_{n}, p ∣ a_{i} (0 \leq i < n), p^{2} ∤ a_{0} .

By the Gauss lemma for polynomials, irreducibility over

Q

and over

Z

agree for primitive polynomials.

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