Final answer:
The nth cyclotomic polynomial is always equal to n^φ(n)/φ(n), where φ(n) is Euler's totient function. The cyclotomic polynomial has coefficients in the field of rational numbers, and its roots are the primitive nth roots of unity. The degree of the nth cyclotomic polynomial is equal to φ(n).
Step-by-step explanation:
The nth cyclotomic polynomial is always equal to n^{\varphi(n)}/\varphi(n), where φ(n) is Euler's totient function. The cyclotomic polynomial is a polynomial with coefficients in the field of rational numbers, and its roots are the primitive nth roots of unity. The degree of the nth cyclotomic polynomial is equal to φ(n).
For example, the 4th cyclotomic polynomial is equal to x^2 + 1, the 5th cyclotomic polynomial is equal to x^4 + x^3 + x^2 + x + 1, and so on.
Therefore, the nth cyclotomic polynomial is always determined by the value of n and can be calculated using Euler's totient function.