grandes-ecoles 2025 Q6b

grandes-ecoles · France · polytechnique-maths-a__mp Not Maths
Prove that there exists a natural integer $n$ such that $X^n \in \mathcal{J}$. Deduce that $\mathcal{J}$ is generated by the monomial $X^r$ for a suitable natural integer $r$ that we do not ask you to specify.
Prove that there exists a natural integer $n$ such that $X^n \in \mathcal{J}$. Deduce that $\mathcal{J}$ is generated by the monomial $X^r$ for a suitable natural integer $r$ that we do not ask you to specify.