Mathematics Tripos Papers

  • Part IA
  • Part IB
  • Part II
  • FAQ

4.I.2G

Groups, Rings and Modules | Part IB, 2008

Let n≥2n \geq 2n≥2 be an integer. Show that the polynomial (Xn−1)/(X−1)\left(X^{n}-1\right) /(X-1)(Xn−1)/(X−1) is irreducible over Z\mathbb{Z}Z if and only if nnn is prime.

[You may use Eisenstein's criterion without proof.]

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