Question

Fie A=2^n+3+2^n+2+2^n,cu n€N. b) Determinati cel mai mic numar n€N, pentru care A este divizibil cu 16

Answer 1

$2^{n+3}+ 2^{n+2} +2^n=2^n*2^3+2^n*2^2+2^n=2^n(2^3+2^2+1)=2^n*13$

13 - numar prim, prin urmare $2^n=16$
$2^n=2^4$
$n=4$