cyclotomic polynomial

== English == === Noun === cyclotomic polynomial (plural cyclotomic polynomials) (algebra) For a positive integer n, a polynomial whose roots are the primitive nth roots of unity, so that its degree is Euler's totient function of n. That is, letting ζ n = e i 2 π / n {\displaystyle \zeta _{n}=e^{i2\pi /n}} be the first primitive nth root of unity, then Φ n ( x ) = ∏ gcd ( n , m ) = 1 1 ≤ m < n ( x − ζ n m ) {\displaystyle \Phi _{n}(x)=\prod _{\stackrel {1\leq m<n}{\gcd(n,m)=1}}(x-\zeta _{n}^{m})} is the nth such polynomial.