Question

Use the Eisenstein Criterion to prove that if is a squarefree integer, then $x^{n}-a$ is irreducible in $\mathbb{Q}[x]$ for every $n\geq 1$ . Conclude that there are irreducible polynomials in $\mathbb{Q}[x]$ of every degree $n\geq 1.$

Answer 1

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if a se all iss square free then no prime factors of a is repented twice. prime factor of a are single distinct prime factor. Then he foss a prime pla, we here, ☺ bola ☺ px 1 in pexa So by Kirenstein Criterion na is boreducible in Q[x] for every nyl. Since it a is any Square free integer , then x² _a is an inedreible polyreial in Qua] for every degre nylo