b) n ^ 4 - n ^ 2 chia hết cho 4 với n nguyên

`#thanhan12345`

`n^4 - n^2 = n^2 . ( n^2 - 1 )`

`= n^2 . ( n - 1 ) . ( n + 1 )`

`\text{+) Nếu n chia hết cho 2 thì : }` `n^2 vdots 4`

`=> n^2 . ( n - 1 ) . ( n + 1 ) vdots 4 `

`\text{+) Nếu n chia cho 2 dư 1 thì :}` ` n - 1 vdots 2 , n + 1 vdots 2 `

`=> ( n - 1 ) . ( n + 1 ) vdots 4`

`=> n^2 . ( n - 1 ) . ( n + 1 ) vdots 4`

`\text{Vậy }` `n^4 - n^2 vdots 4` `\text{với n nguyên .}`