[tex]3^{0}+3^{1}+3^{2}=1+3+9=13[/tex]
[tex]a=3+3^{2}+3^{3}+....+3^{2013}
[/tex]
impartim aceasta suma in grupe de catre 3 termeni
cum in suma sunt 2013 termeni -> 2013/3=671 grupe
[tex]a=(3+3^{2}+3^{3})+(3^{4}+3^{5}+3^{6})+...+(3^{2011}+3^{2012}+3^{2013})[/tex][tex]a=3(3^{0}+3^{1}+3^{2})+3^{4}(3^{0}+3^{1}+3^{2})+...+3^{2011}(3^{0}+3^{1}+3^{2})[/tex]
[tex]a=3*13+3^{4}*13+.....+3^{2011}*13[/tex]
[tex]a=13(3+3^{4}+...+3^{2011})[/tex]
rezulta ca a e multiplu de 13 -> 13 divide a
