Question

Aratati ca oricare ar fi n un numar natural numarul a=3 la puterea 2n+1 + 3 la puterea 2n × 2 la puterea 2 este divizibil cu 7.

Answer 1

$a=3^{2n+1}+3^{2n}\cdot2^{2}$
$a=3^{2n}\cdot3+3^{2n}\cdot4$
$a=3^{2n}(3+4)=3^{2n}\cdot7~\vdots~7$