1. The problem statement, all variables and given/known data So I need the find the minimal polynomial of the primitive 15th root of unity. Let's call this minimal polynomial m(x) 2. Relevant equations 3. The attempt at a solution I know that m(x) is an irreducible factor of x^15 - 1 and also that the degree of m(x) is equal to the Euler function (e), and e(15) = 8, so m(x) will have degree 8. I also know that given one of the primitive roots of unity, call it c, that c^7+c^6+c^5+c^4+c^3+c^2+c+1 = 0. Where can I go from here to find m(x) over Q? perhaps multiplying together (x-c^7)(x-c^6)(x-c^5)......(x-1) will give me it? Is there a faster way than this? Thanks PF!