Đk: ` n ∈ Z `
` n - 4 \vdots n^2 + 1 `
` => (n - 4)^2 \vdots n^2 + 1`
` => n^2 + 2n^2 . 4 - 4^2 \vdots n^2 + 1 `
` => n^2 + 8n^2 - 16 \vdots n^2 + 1 `
` => 9n^2 - 16 \vdots n^2 + 1 `
` => 9n^2 + 9 - 25 \vdots n^2 + 1 `
Vì ` 9n^2 + 9 \vdots n^2 + 1 `
` => -25 \vdots n^2 + 1 `
` => n^2 + 1 ∈ Ư(-25) = { ±1 ; ±5 ; ±25 } `
` => n^2 ∈ {-2 ; 0 ; -6 ; 4 ; -26 ; 24} `
` => n^2 ∈ {0 ; 4 ; 24} `
` => n ∈ {0 ; 2} `