P r o b l e m a : {\displaystyle Problema:} Fie K {\displaystyle K} un corp cu m ≥ 2 {\displaystyle m\geq 2} elemente si f ∈ K [ X ] {\displaystyle f\in K[X]} . Aratati ca urmatoarele afirmatii sunt echivalente: ( i ) E x i s t a < m a t h > g ∈ K [ X ] {\displaystyle (i)Exista<math>g\in K[X]} astfel incat f ( X ) = g ( X m − 1 ) {\displaystyle f(X)=g(X^{m-1})} ;
(ii) Pentru orice a ∈ K ∗ {\displaystyle a\in K^{*}} avem f ( X ) = f ( a X ) {\displaystyle f(X)=f(aX)} .
\end{enumerate}</math>
![{\displaystyle f\in K[X]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b6ec2d50f6317a5098e90e7e9742f89a1f133824)
![{\displaystyle (i)Exista<math>g\in K[X]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/99c3cee9d27239b0596050b12f0e4422be77065f)
