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?

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