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}
