CM: A chia hết cho 13 A=3 mũ 11+3 mũ 12+3 mũ 13+3 mũ14+3 mũ 15+3 mũ 16 10/08/2021 Bởi Everleigh CM: A chia hết cho 13 A=3 mũ 11+3 mũ 12+3 mũ 13+3 mũ14+3 mũ 15+3 mũ 16
\(\begin{array}{l}A = {3^{11}} + {3^{12}} + {3^{13}} + {3^{14}} + {3^{15}} + {3^{16}}\\\,\,\,\,\, = {3^{11}}\left( {1 + 3 + {3^2}} \right) + {3^{14}}\left( {1 + 3 + {3^2}} \right)\\\,\,\,\, = {3^{11}}.\,13 + {3^{14}}.13\\\,\,\,\, = \,13.\left( {{3^{11}} + {3^{14}}} \right)\\ \Rightarrow A \vdots \,13\end{array}\) Bình luận
\(\begin{array}{l}A = {3^{11}} + {3^{12}} + {3^{13}} + {3^{14}} + {3^{15}} + {3^{16}}\\\,\,\,\,\, = {3^{11}}\left( {1 + 3 + {3^2}} \right) + {3^{14}}\left( {1 + 3 + {3^2}} \right)\\\,\,\,\, = {3^{11}}.\,13 + {3^{14}}.13\\\,\,\,\, = \,13.\left( {{3^{11}} + {3^{14}}} \right)\\ \Rightarrow A \vdots \,13\end{array}\)