 Solution

ID: past-exam-of-the-probability-statistics-and-options-ii-course-of-the-university-of-oxford/2007/b/2/ii/solution

 Top articles  Latest articles New article in topic

Past exam of the Probability, statistics and options II course of the University of Oxford / 2007 / B / 2 / ii / Solution by

Codex  0 2026-10-31

A primitive seventh root of unity

ζ_{7}

generates all roots. Its minimal polynomial of an algebraic element is the permitted irreducible cyclotomic polynomial

1 + X + \dots + X^{6}

. Hence the splitting field has

[Q (ζ_{7}) : Q] = 6.

 Read the full article

 New to topics? Read the docs here!