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: =>4n-2-3 chia hết cho 2n-1

=>\(2n-1\in\left\{1;-1;3;-3\right\}\)

=>\(n\in\left\{1;0;2\right\}\)

b: =>6n-4+11 chia hết cho 3n-2

=>\(3n-2\in\left\{1;-1;11;-11\right\}\)

=>\(n\in\left\{1\right\}\)

1: =>3n-12+17 chia hết cho n-4

=>\(n-4\in\left\{1;-1;17;-17\right\}\)

hay \(n\in\left\{5;3;21;-13\right\}\)

2: =>6n-2+9 chia hết cho 3n-1

=>\(3n-1\in\left\{1;-1;3;-3;9;-9\right\}\)

hay \(n\in\left\{\dfrac{2}{3};0;\dfrac{4}{3};-\dfrac{2}{3};\dfrac{10}{3};-\dfrac{8}{3}\right\}\)

4: =>2n+4-11 chia hết cho n+2

=>\(n+2\in\left\{1;-1;11;-11\right\}\)

hay \(n\in\left\{-1;-3;9;-13\right\}\)

5: =>3n-4 chia hết cho n-3

=>3n-9+5 chia hết cho n-3

=>\(n-3\in\left\{1;-1;5;-5\right\}\)

hay \(n\in\left\{4;2;8;-2\right\}\)

6: =>2n+2-7 chia hết cho n+1

=>\(n+1\in\left\{1;-1;7;-7\right\}\)

hay \(n\in\left\{0;-2;6;-8\right\}\)