Question

Arata ca (5 la puterea n * 2 la puterea n +8) este divizibil cu 3, oricare ar fi n natural.

Answer 1

$\it a=5^n\cdot2^n+8=(5\cdot2)^n+8=10^n+8=1\underbrace{000... 0}_{n\ zerouri}+8=\\ \\ \\ =1\underbrace{000\ ...\ 0}_{n-1\ zerouri}8\ \in\ M_3 \Rightarrow a\ \vdots\ 3,\ pentru\ oricare\ n\in\mathbb{N}.$