Question

Am problema:
Aratati ca numarul N= $3^{n+2}$·$2^{2n+3}$+$3^{n+3}$·$4^{n+2}$ , este divizibil cu 63

Answer 1

$...=3^{n+2}\cdot2^{2n+3}+3^{n+3}\cdot2^{2n+4}=3^{n+2}\cdot2^{2n+3}\cdot(1+3\cdot2)=$

$=3^n\cdo9\cdot2^{n+3}\cdot7=63\cdot3^n\cdot2^{n+3}\vdots63$