Question

aratati ca 15 la puterea 2n+1 - 5 la puterea 2n * 9 la puterea n+1 se divide cu 90 oricare ar fi n apartine nr natural va rog repede​

Answer 1

$\it 15^{2n+1}-5^{2n}\cdot9^{n+1}=15^{2n}\cdot15-5^{2n}\cdot3^{2n}\cdot9=15^{2n}(15-9)=\\ \\ =15^{2n}\cdot6=15^{2n-1}\cdot15\cdot6=15^{2n+1}\cdot90\in M_{90} \Rightarrow (15^{2n+1}-5^{2n}\cdot9^{n+1})\ \vdots\ 90$

Answer 2

Răspuns:

Explicație pas cu pas: