Chứng minh rằng:
\(2^{10}+2^{11}+2^{12}\)
\(=2^{10}\left(1+2+2^2\right)\)
\(=2^{10}.7\) \(⋮\) 7
Vậy \(2^{10}+2^{11}+2^{12}\) chia hết cho 7
Chứng minh rằng:
\(3^{n+3}+3^{n+2}+2^{n+3}+2^{n+2}\)
\(=3^n.3^3+3^n.3^2+2^n.2^3+2^n.2^2\)
\(=3^n\left(3^3+3^2\right)+2^n\left(2^3+2^2\right)\)
\(=36.3^n+12.3^n\)
\(=6\left(6.3^n+2.3^n\right)\) \(⋮\) 6 với mọi n \(\in\) N
Vậy \(3^{n+3}+3^{n+2}+2^{n+3}+2^{n+2}\) chia hết cho 6 với mọi n \(\in\) N
Chứng minh rằng:
\(81^7-27^9-9^{13}\)
\(=\left(3^4\right)^7-\left(3^3\right)^9-\left(3^2\right)^{13}\)
\(=3^{28}-3^{27}-3^{26}\)
\(=3^{24}\left(3^4-3^3-3^2\right)\)
\(=3^{24}.45\) \(⋮\) 45
Vậy \(81^7-27^9-9^{13}\) chia hết cho 45
