Question

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Answer 1

Răspuns:

Explicație pas cu pas:

b = 1+3 +3^2 + 3^3(1+3+3^2) + 3^6(1+3+3^2) +...

3^114(1+3+3^2) = 13 +3^3*13 +3^6*13+...+3^114*13 =

13*(1 +3^3 +3^6+ ...+ 3^114) = m(13) multiplu de 13

Answer 2

Explicație pas cu pas:

$B = 1+{3}^{1}+{3}^{2}+{3}^{3}+...+{3}^{116}$

$B=\big({3}^{0}+{3}^{1}+{3}^{2}\big) + \big({3}^{3} +{3}^{4}+ {3}^{5} \big)+...+\big({3}^{114}+{3}^{115}+{3}^{116} \big)$

$B=\big({3}^{0}+{3}^{1}+{3}^{2}\big)+{3}^{3}\cdot\big({3}^{3-3} +{3}^{4-3}+ {3}^{5-3}\big)+...+{3}^{114}\cdot\big({3}^{114 -114}+{3}^{115-114}+{3}^{116-114}\big)$

$B=\big(1+3+9\big)+{3}^{3}\cdot\big({3}^{0}+{3}^{1}+{3}^{2}\big)+...+{3}^{114}\cdot\big({3}^{0}+{3}^{1}+{3}^{2}\big)$

$B=13+{3}^{3}\cdot13+ {3}^{6} \cdot13 +...+{3}^{114}\cdot13$

Dăm factor comun pe 13

$B=13\cdot\big({3}^{3}+{3}^{6}+...+{3}^{114}\big) \Rightarrow\underline{B \: \vdots\:13}$