Cyclotomic Polynomials
(Wikipedia)(MathWorld)

We define radical(n) as the greatest squarefree divisor of n.


Phi(n)(x) = Phi(radical(n))(x^r), where r = n/radical(n) 
We can use this identity to reduce any cyclotomic polynomial to its radical

Phi45(x) = Phi(3*15)(x) = Phi15(x^3)
Phi75(x) = Phi(5*15)(x) = Phi15(x^5)


We can reduce it further when n is even, using this identity:
Phi(2n)(x) = Phi(n)(-x), where n is odd

Phi12(x) = Phi(2*6)(x) = Phi6(x^2) = Phi3(-x^2)
Phi18(x) = Phi(3*6)(x) = Phi6(x^3) = Phi3(-x^3)
Phi36(x) = Phi(6*6)(x) = Phi6(x^6) = Phi3(-x^6)

Phi60(x) = Phi(2*30)(x) = Phi30(x^2) = Phi15(-x^2)