Question

Aratati ca 2 | ( 1^{n} + 2^{n} + 3^{n} , pentru orice n .N numar natural nenul.Dau 13 puncte.

Answer 1

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