grandes-ecoles 2019 Q3

grandes-ecoles · France · x-ens-maths1__mp Number Theory Algebraic Number Theory and Minimal Polynomials

(a) Show that $\Pi _ { \alpha }$ is irreducible in $\mathbb { Q } [ X ]$.
(b) Let $P \in \mathbb { Q } [ X ]$ be a monic polynomial, irreducible in $\mathbb { Q } [ X ]$. Show that if $z$ is a complex root of $P$, then $P$ is the minimal polynomial of $z$.

(a) Show that $\Pi _ { \alpha }$ is irreducible in $\mathbb { Q } [ X ]$.\\
(b) Let $P \in \mathbb { Q } [ X ]$ be a monic polynomial, irreducible in $\mathbb { Q } [ X ]$. Show that if $z$ is a complex root of $P$, then $P$ is the minimal polynomial of $z$.

Paper Questions

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