Question

aratati ca 6 este divizibil cu 1+5+5 la 2+....+5 la 2013

Answer 1

$\boxed{1+5=6}$
$1+5+5^2+5^3+...+5^{2013} \\ \\ =(1+5)+(5^2+5^3)+...+(5^{2012}+5^{2013}) \\ \\ =(1+5)+5^2(1+5)+...+5^{2012}(1+5) \\ \\ =6+5^2\cdot6+...+5^{2012}\cdot6 \\ \\ =6(1+5^2+...+5^{2012})~\vdots~6$