a,Ta có:3n+24 chia hết cho n-4

=>3n-12+36 chia hết cho n-4

=>3(n-4)+36 chia hết cho n-4

Mà 3(n-4) chia hết cho n-4

=>36 chia hết cho n-4

=>n-4\(\in\)Ư(36)={-36,-18,-12,-9,-6,-4,-3,-2,-1,1,2,3,4,6,9,12,18,36}

=>n\(\in\){-32,-14,-8,-5,-2,0,1,2,3,5,6,7,8,10,13,16,22,40}

n,n-6 chia hết cho n-1

=>n-1-5 chia hết cho n-1

Mà n-1 chia hết cho n-1

=>5 chia hết cho n-1

=>n-1\(\in\)Ư(5)={-5,-1,1,5}

=>n\(\in\){-4,0,2,6}

a, Ta có : \(3n+2⋮n-1\)

Lại có : \(\left(n-1\right)⋮\left(n-1\right)\)

nên \(3\left(n-1\right)⋮\left(n-1\right)\)

hay \(\left(3n-3\right)⋮\left(n-1\right)\)

Suy ra : \(\left(3n+2\right)-\left(3n-3\right)⋮\left(n-1\right)\)

hay \(3n+2-3n+3⋮\left(n-1\right)\)

\(5⋮\left(n-1\right)\)

\(\Rightarrow\left(n-1\right)\inƯ\left(5\right)=\left\{1;5\right\}\)

+ Nếu n - 1 = 5 => n = 6

+ Nếu n - 1 = 1 => n = 0

Làm đc câu 1 thôi nha , còn đâu cứ dựa vào đấy mà làm 

a) ta có

3n+2

=3n-3+5

=(n-1)3+5

để 3n+2chia hết cho n-1 thì (n-1)3+5chia hết cho n-1

mà 3(n-1)chia hết cho n-1 nên 5 chia hết cho n-1

=>n-1 thuộc ước của 5

=>n-1 thuộc {1,-1,-5,5}

=> n thuộc {2,0,-4,6}

b) tương tự

c)n²

=n²-1+1

=(n+1)(n-1)+1

để n² chia hết cho n+1

thì (n+1)(n-1)+1chia hết cho n+1

mà (n+1)(n-1) chia hết cho n+1

nên 1 chia hết cho n+1

=>n+1 thuộc {1,-1}

=>n thuộc {0-2}

thick nha

Còn cả các số đối nữa nên kq có thêm 2 đ/s là 2 và -4

a: \(\Leftrightarrow10n^2+25n-16n-40+43⋮2n+5\)

\(\Leftrightarrow2n+5\in\left\{1;-1;43;-43\right\}\)

hay \(n\in\left\{-2;-3;19;-24\right\}\)

b: \(\Leftrightarrow7n^2+9n-4⋮3n+5\)

\(\Leftrightarrow21n^2+27n-12⋮3n+5\)

\(\Leftrightarrow21n^2+35n-8n-\dfrac{40}{3}+\dfrac{4}{3}⋮3n+5\)

\(\Leftrightarrow3n+5\in\left\{1;-1;2;-2;4;-4\right\}\)

hay \(n\in\left\{-2;-1;-3\right\}\)

\(a,2n+3⋮6n+4\Leftrightarrow6n+9⋮6n+4\Leftrightarrow6n+9-6n-4⋮6n-4\Leftrightarrow5⋮6n-4\Leftrightarrow6n-4\in\left\{-5;5;1;-1\right\}\Leftrightarrow6n\in\left\{-1;9;5;-3\right\}\Leftrightarrow n\in\left\{-\dfrac{1}{6};1,5;\dfrac{5}{6};-0,5\right\}\)

ta có 343=7^3

vì 9n^3 không chia hết cho 7

vì 9n^2 không chia hết cho 7

vì 3n  không chia hết cho 7

vì 16  không chia hết cho 7

=> 9n^3+9n^2+3n-16 không chia hết cho 343

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