Not as complex as it looks

Number Theory Level 4

For any positive integer \(n\), we define the cyclotomic polynomial \(\Phi_n(x)=\prod(x-w)\), where the product is taken over all primitive \(n\)th roots of unity, \(w\).

Which of the statements (a), (b), (c), (d), (e), in this order, is the FIRST to be true?

All coefficients of all cyclotomic polynomials are

(a) 0, 1, or -1

(b) integers

(c) rational

(d) real

(e) complex


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