Question

Tìm số nguyên n , biết:

5) 2n + 7 \(⋮\) n + 1

6) 2n + 9 \(⋮\) n - 3

Answer 1

\(2n+7⋮n+1\)

\(\Rightarrow2n+2+5⋮n+1\)

\(\Rightarrow2\left(n+1\right)+5⋮n+1\)

Vì \(2\left(n+1\right)⋮n+1\) nên để \(2\left(n+1\right)+5⋮n+1\) thì \(5⋮n+1\)

\(\Rightarrow n+1\inƯ\left(5\right)=\left\{\pm1;\pm5\right\}\)

n + 1	1	-1	5	-5
n	0	-2	4	-6

Vậy n = {0;-2;4;-6}

\(2n+9⋮n-3\)

\(\Rightarrow2n-6+15⋮n-3\)

\(\Rightarrow2\left(n-3\right)+15⋮n-3\)

Vì \(2\left(n-3\right)⋮n-3\) nên để \(2\left(n-3\right)+15⋮n-3\) thì \(15⋮n-3\)

\(\Rightarrow n-3\inƯ\left(15\right)=\left\{\pm1;\pm3;\pm5;\pm15\right\}\)

n - 3	1	-1	3	-3	5	-5	15	-15
n	4	2	6	0	8	-2	18	-12

Vậy n = {4;2;6;0;8;-2;18;-12}