Question

.Aratati ca 2|(1^n+2^n+3^n), pentru orice n N*

Answer 1

$n \in N^* \Rightarrow \\ \Rightarrow 1 ^n=1-impar \\ \Rightarrow 2^n-par \\ \Rightarrow3^n-impar \\ \\ 1^n+2^n+3^n=(impar)+(par)+(impar) =(par) \\ \\ Deci~2~|~(1^n+2^n+3^n).$