# Algebraic Number Theory

Explain why the polynomial H(x) = x^5 + x^4 + x^3 + x^2 + 1 is irreducible over the integers.

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Update:

I noted the restrictions on the method to be used for solving this question.

The problem can be easily solved using the Rational Roots Theorem alone (Without using Descartes' Rule of Signs) as ...

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Explanation of why the given polynomial is irreducible over integers using the Rational Roots Theorem.

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