Đáp án:
`n ∈` `{1; 1/3; 3; -5/3}`
Giải thích các bước giải:
`Tìm` `n:`
`(3n³+13n²-7n+5):(3n-2)`
`text{Ta có:}`
`⇔A=3n³+13n²-7n+5`
`⇔A=3n³-2n²+15n²-10n+3n+5`
`⇔A=n²` $\times$ `(3n-2)+5n` $\times$ `(3n-2)+3n+5`
`text{Ta lại có:}`
Muốn `A` $\vdots$ `3n-2`
`⇔3n+5:3n-2`
`⇔3n+5-(3n-2):3n-2`
`⇔7:3n-2`
`⇔3n-2 ∈ Ư7`
`⇔3n-2 ∈ {` $\pm$ `1` `;` $\pm$ `7}`
`⇔3n ∈ {3; 1; 9; -5}`
`⇔n ∈` `{1; 1/3; 3; -5/3}`
