Đáp án + Giải thích các bước giải:
`a//` Để `(n+10)/(2n-8)∈Z`
`⇒n+10` $\vdots$ `2n-8`
`⇒2(n+10)` $\vdots$ `2n-8`
`⇒2n+20` $\vdots$ `2n-8`
`⇒(2n-8)+28` $\vdots$ `2n-8`
`⇒28` $\vdots$ `2n-8`
`⇒2n-8∈Ư(28)={±1;±2;±4;±7;±14;±28}`
`⇒2n∈{9;10;12;15;22;36;7;6;4;1;-6;-20}`
Mà `n∈N`
`⇒n∈{5;6;11;18;3;2}`
`b//`
Để `(21n+3)/(6n+4)∈Z`
`⇒21n+3` $\vdots$ `6n+4`
`⇒2(21n+3)` $\vdots$ `6n+4`
`⇒42n+6` $\vdots$ `6n+4`
`⇒7(6n+4)-22` $\vdots$ `6n+4`
`⇒22` $\vdots$ `6n+4`
`⇒6n+4∈Ư(22)={±1;±2;±11;±22}`
`⇒6n∈{-3;-2;7;18;-5;-6;-15;-26}`
Mà `n∈N`
`⇒n=3`
