a) \(3n+19⋮n+1\)

\(\Rightarrow\)\(3\left(n+1\right)+16⋮n+1\)

mà \(3\left(n+1\right)⋮n+1\)\(\Rightarrow\)\(16⋮n+1\)

\(\Rightarrow\)\(n+1\in\left\{1,-1,2,-2,4,-4,8,-8,16,-16\right\}\)

\(\Rightarrow n\in\left\{0,-2,1,-3,3,-5,7,-9,15,-17\right\}\)

b) \(2n+7⋮n+2\)

\(\Rightarrow2\left(n+2\right)+3⋮n+2\)

mà \(2\left(n+2\right)⋮n+2\Rightarrow3⋮n+2\)

\(\Rightarrow n+2\in\left\{1,3,-1,-3\right\}\)

\(\Rightarrow n\in\left\{-1,1,-3,-5\right\}\)

c)\(6n+39⋮2n+1\Rightarrow3\left(2n+1\right)+36⋮2n+1\)

mà\(3\left(2n+1\right)⋮2n+1\)\(\Rightarrow36⋮2n+1\)

\(\Rightarrow2n+1\in\left\{1,-1,2,-2,3,-3,4,-4,6,-6,9,-9,12,-12,18,-18,36,-36\right\}\)

\(\Rightarrow2n\in\left\{0,-2,1,-3,2,-4,3,-5,5,-7,8,-10,11,-13,17,-19,35,-37\right\}\)

\(\Rightarrow\)\(n\in\left\{0,-1,1,-2,4,-5\right\}\)

De 6n+7 chia het cho 2n-1

thi 6n+7 chia het cho 2n-1 va 2n-1 chia het cho 2n-1

=> 6n+7 chia het cho 2n-1 va 3.(2n-1) chia het cho 2n-1

=> 6n+7 chia het cho 2n-1 va 6n-3 chia het cho 2n-1

=> (6n+7)-(6n-3) chia het cho 2n-1

=> 6n+7-6n+3 chia het cho 2n-1

=> 10 chia het cho 2n-1

=> 2n-1 thuoc U(10)={1, -1, 2, -2, 5, -5, 10, -10}

phan con lai ban tu lam tiep nhe

Vì 6n + 7 ⋮ 2n - 1 ⇒ 2n + 2n + 2n - 1 - 1 - 1 + 10 ⋮ 2n  1

 ⇒ ( 2n - 1 ) + ( 2n - 1 ) + ( 2n - 1 ) + 10 ⋮ 2n - 1

Vì 2n - 1 ⋮ 2n - 1 . Để ( 2n - 1 ) + ( 2n - 1 ) + ( 2n - 1 ) + 10 ⋮ 2n - 1 ⇒ 10 ⋮ 2n - 1

⇒ 2n - 1 ∈ Ư ( 10 )

⇒ Ư ( 10 ) = { + 1 ; + 2 ; + 5 ; + 10 }

⇒ 2n - 1 = + 1 ; + 2 ; + 5 ; + 10

⇒ 2n = 2 ; 0 ; 3 ; - 1 ; 6 ; - 4 ; 11 ; - 9

 ⇒ n = 1 ; 0 ; 3 ; - 2 

 Vậy n = { - 2 ; 0 ; 1 ; 3 }

a, \(2n+7⋮n+1\)

\(2\left(n+1\right)+5⋮n+1\)

\(5⋮n+1\)hay \(n+1\inƯ\left(5\right)=\left\{\pm1;\pm5\right\}\)

b, \(4n+9⋮2n+3\)

\(2\left(2n+3\right)+3⋮2n+3\)

\(3⋮2n+3\)hay \(2n+3\inƯ\left(3\right)=\left\{\pm1;\pm3\right\}\)

4-3=2 yêu anh ko hề sai

n+ 9 \(⋮n-2\)

mà n - 2 \(⋮n-2\)

= n -2 +11 \(⋮n-2\)

=> 11 \(⋮n-2\)

n -2 \(\inư\left(11\right)\in1,11\)

Ta có bảng: 

Vậy x = 3; 13

Thanks bạn nha !!!!!!!!!!! Kb vs mk nha!!!!!!!!!!!!