Question

A=2n+4x3n+2nx3n+2 se divide cu 150.

Answer 1

Explicație pas cu pas:

$A = {2}^{n + 4} \cdot {3}^{n} + {2}^{n} \cdot {3}^{n + 2} = {2}^{4} \cdot {2}^{n} \cdot {3}^{n} + {2}^{n} \cdot {3}^{n} \cdot {3}^{2} = 16 \cdot {(2 \cdot 3)}^{n} + 9 \cdot {(2 \cdot 3)}^{n} = 16 \cdot {6}^{n} + 9 \cdot {6}^{n} = {6}^{n} \cdot (16 + 9) = {6}^{n} \cdot 25 = {6}^{n - 1} \cdot 6 \cdot 25 = {6}^{n - 1} \cdot 150$

$\implies \bf A \ \ \vdots \ 150$

q.e.d.