Question

Chứng tỏ:

81⁷-27⁹-9¹³\(⋮\)405

Answer 1

81^7-27^9-9^13 

=(3^4)^7-(3^3)^9-(3^2)^13 

=3^28-3^27-3^26 

=(3^26.3^2)-(3^26.3^1)-(3^26.1) 

=3^26.(9-3-1) 

=3^22.(3^4.5) 

=3^22.405 chia het cho 405 

=> 81^7-27^9-9^13 chia het cho 405

Answer 2

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

\(=3^{28}-3^{27}-3^{36}=3^{22}.\left(3^6-3^5-3^4\right)\)

\(=3^{22}.405⋮405\)