+)Ta có:\(A=2019+2019^2+2019^3+2019^4+2019^5+2019^6\)

\(\Rightarrow A=\left(2019+2019^2\right)+\left(2019^3+2019^4\right)+\left(2019^5+2019^6\right)\)

\(\Rightarrow A=\left(2019+2019^2\right)+2019^2.\left(2019+2019^2\right)+2019^4.\left(2019+2019^2\right)\)

+)Ta lại có:2019² tận cùng là 1

=>2019+2019² tân cùng là 9+1=10

=>2019+2019²\(⋮2\)

\(\Rightarrow\left(2019+2019^2\right)⋮2;2019^2.\left(2019+2019^2\right)⋮2;2019^4.\left(2019+2019^2\right)⋮2\)

\(\Rightarrow A⋮2\)

Vậy \(A⋮2\left(ĐPCM\right)\)

Chúc bn học tốt

A = 2019 + 2019² + 2019³ + 2019⁴ + 2019⁵ + 2019⁶

A = ( 2019 + 2019² ) + ( 2019³ + 2019⁴) + ( 2019⁵ + 2019⁶)

A = 1 . ( 2019 + 2019² ) + 2019³ . (2019 + 2019² ) + 2019⁵ . ( 2019 + 2019² )

A = 1 . 4 078 380   + 2019³ . 4 078 380 + 2019⁵ . 4 078 380

A = 4 078 380 . ( 1 + 2019³ + 2019⁵) \(⋮2\rightarrowĐPCM\)

# HOK TỐT #

Xin chào bạn ! Mình là youtuber PUBG Takaz đây !

\(2019^{2019}-1=2019^{2019}-1^{2019}⋮2019-1=2018⋮2018\)

Ta có: 35²⁰¹⁹-35²⁰¹⁸ = 35²⁰¹⁸(35-1)

= 35²⁰¹⁸.34

Vì 34 chia hết cho 17 nên suy ra 35²⁰¹⁸.34 chia hết cho 17

Vậy 35²⁰¹⁹-35²⁰¹⁸ chia hết cho 17.