Question

Aratati ca numarul N= 7^n x 9^n + 21^n+1 x 3^n - 9 x 63^n este divizibil cu 13, pentru orice numjar natural

Answer 1

$=7^n*9^n+21^n*21*3^n-9*63^n=7^n*3^n*3^n+7^n*3^n*21*3^n-$
$-9*3^n*3^n*7^n=3^n*3^n*7^n(1+21-9)=3^n*3^n*7^n*13$