Question

Chứng minh rằng:

1/ 8⁷ - 2¹⁸ chia hết cho 14

2/ 7⁶ +7⁵ - 9¹³ chia hết cho 55

3/ 81⁷ - 27⁹ - 9¹³ chia hết cho 405

Answer 1

1) \(8^7-2^{18}=\left(2^3\right)^7-2^{18}=2^{21}-2^{18}=2^{17}\left(2^4-2\right)=2^{17}.14⋮14\)

vậy đpcm

3) \(81^7-27^9-9^{13}=\left(3^4\right)^7-\left(3^3\right)^9-\left(3^2\right)^{13}=3^{28}-3^{27}-3^{26}\)

\(=3^{22}\left(3^6-3^5-3^4\right)=3^{22}.405⋮405\)

vậy đpcm

Answer 2

2: Sửa đề: 7^6+7^5-7^4

=7^4(7^2+7-1)

=7^4*55 chia hết cho 55

3: \(=3^{28}-3^{27}-3^{26}=3^{26}\left(3^2-3-1\right)=3^{26}\cdot5\)

\(=3^{22}\cdot405⋮405\)

1: \(=2^{21}-2^{18}=2^{17}\left(2^4-2\right)=2^{17}\cdot14⋮14\)