Let K {\displaystyle {}K} be a field, and let K [ X ] {\displaystyle {}K[X]} be the polynomial ring over K {\displaystyle {}K} . Let P = X n ∈ K [ X ] {\displaystyle {}P=X^{n}\in K[X]} with n ≥ 1 {\displaystyle {}n\geq 1} . Show that all normed divisors of P {\displaystyle {}P} have the form X k {\displaystyle {}X^{k}} , 1 ≤ k ≤ n {\displaystyle {}1\leq k\leq n} .
![{\displaystyle {}K[X]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7861df9df3d7463835d927c4d0d4c27f5e2f8416)
![{\displaystyle {}P=X^{n}\in K[X]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d2410520b905fef768376b8e120054b1838983df)
