Question

GIÚP E VS 7H20 E ĐI HCỌ GÒI

Chứng minh rằng:

81^7 - 27^9 - 9^13 chia hết cho 15

Answer 1

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

\(=3^{26}\left(3^2-3-1\right)=3^{26}.5⋮5\)

Answer 2

\(=3^{25}.15⋮15\)

Answer 3

Đặt A = 81⁷ - 27⁹ - 9¹³

= (3⁴)⁷ - (3³)⁹ - (3²)¹³

= 3²⁸ - 3²⁷ - 3²⁶

= 3²⁵.(3³ - 3² - 3)

= 3²⁵.(27 - 9 - 3)

= 3²⁵.15 ⋮ 15

Vậy A ⋮ 15