# Counting Irreducible Polynomials

Algebra Level 5

Let $$P_{n}(x) = x^{n}+x^{n-1}+...+x^{2}+x+1$$ for integral $$n$$. How many values of $$n \in [1,100]$$ are there such that $$P_{n}(x)$$ is irreducible over the rational numbers?

×