2015-12-4

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Problema:} Fie Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle K} un corp cu $m\geq 2$ elemente si $f\in K[X]$. Aratati ca urmatoarele afirmatii sunt echivalente:

(i) Exista $g\in K[X]$ astfel incat $f(X)=g(X^{m-1})$;

(ii) Pentru orice $a\in K^{*}$ avem $f(X)=f(aX)$.

$Solutie$ Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (i) \rightarrow (ii)} Din teorema lui Lagrange aplicata grupului Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (K^*,\cdot)} avem ca