cyclotomic polynomial

Noun

For a positive integer n, a polynomial whose roots are the primitive n^th roots of unity, so that its degree is the Euler's totient function of n. In symbols, letting $\zeta_n = e^{i 2 \pi / n}$ be the first primitive n^th root of unity, then $\Phi_n(x) = \prod_\stackrel{1 \le m < n}{\gcd(n,m) = 1} (x - \zeta_n^m)$ is the n^th such polynomial.

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