Explicație pas cu pas:
[tex]B = 1+{3}^{1}+{3}^{2}+{3}^{3}+...+{3}^{116} [/tex]
[tex]B=\big({3}^{0}+{3}^{1}+{3}^{2}\big) + \big({3}^{3} +{3}^{4}+ {3}^{5} \big)+...+\big({3}^{114}+{3}^{115}+{3}^{116} \big)[/tex]
[tex]B=\big({3}^{0}+{3}^{1}+{3}^{2}\big)+{3}^{3}\cdot\big({3}^{3-3} +{3}^{4-3}+ {3}^{5-3}\big)+...+{3}^{114}\cdot\big({3}^{114 -114}+{3}^{115-114}+{3}^{116-114}\big)[/tex]
[tex]B=\big(1+3+9\big)+{3}^{3}\cdot\big({3}^{0}+{3}^{1}+{3}^{2}\big)+...+{3}^{114}\cdot\big({3}^{0}+{3}^{1}+{3}^{2}\big)[/tex]
[tex]B=13+{3}^{3}\cdot13+ {3}^{6} \cdot13 +...+{3}^{114}\cdot13[/tex]
Dăm factor comun pe 13
[tex]B=13\cdot\big({3}^{3}+{3}^{6}+...+{3}^{114}\big) \Rightarrow\underline{B \: \vdots\:13}[/tex]
