Tìm số nguyên n: a)n+7 chia hết cho n+2 b)9-n chia hết cho n-3 c)n^2+n+17 chia hết cho n+1 d)n^2 +25 chia hết cho n+2

a, Ta có: n+7$\vdots$n+2

⇒n+2+5$\vdots$n+2

⇒n+2∈Ư(5)={±1;±5}

n+2=1⇒n=-1

n+2=-1⇒n=-3

n+2=5⇒n=3

n+2=-5⇒n=-7

Vậy n∈{-1;-3;3;-7}

b, Ta có: 9-n$\vdots$n-3

⇒-(n-3)+6$\vdots$n-3

⇒n-3∈Ư(6)={±1;±2;±3;±6}

n-3=-6⇒n=-3

n-3=-3⇒n=0

n-3=-2⇒n=1

n-3=-1⇒n=2

n-3=1⇒n=4

n-3=2⇒n=5

n-3=3⇒n=6

n-3=6⇒n=9

Vậy n={0,1,2,-3,4,5,6,9}

c, Ta có: n²+n+17$\vdots$n+1

⇒n(n+1)+17$\vdots$n+1

⇒n+1∈Ư(17)={±1;±17}

n+1=-17⇒n=-18

n+1=-1⇒n=-2

n+1=1⇒n=0

n+1=17⇒n=16

Vậy n={-18,-2,0,16}

d, Ta có: n²+25$\vdots$n+2

⇒n²-4-21$\vdots$n+2

⇒(n-2)(n+2)-21$\vdots$n+2

⇒n+2∈Ư(21)={±1;±3;±7;±21}

n+2=-21⇒n=-23

n+2=-7⇒n=-9

n+2=-3⇒n=-5

n+2=-1⇒n=-3

n+2=1⇒n=-1

n+2=3⇒n=1

n+2=7⇒n=5

n+2=21⇒n=19

Vậy n={-23,-9,-5,-3,-1,1,5,19}

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