Question

tìm tất cả số tự nhiên n sao cho:
a)3.n +10chia hết cho n+1 c) n+12 chia hết cho n+2
b) n+7 chia hết cho n+2 d) 2.n+ 3chia hết cho n-1

Answer 1

a: \(\Leftrightarrow3n+3+7⋮n+1\)

\(\Leftrightarrow n+1\in\left\{1;-1;7;-7\right\}\)

hay \(n\in\left\{0;6\right\}\)

b: \(\Leftrightarrow n+2+5⋮n+2\)

\(\Leftrightarrow n+2\in\left\{1;-1;5;-5\right\}\)

hay n=3

c: \(\Leftrightarrow n+2+10⋮n+2\)

\(\Leftrightarrow n+2\in\left\{1;-1;2;-2;5;-5;10;-10\right\}\)

hay \(n\in\left\{0;3;8\right\}\)

d: \(\Leftrightarrow2n-2+5⋮n-1\)

\(\Leftrightarrow n-1\in\left\{1;-1;5;-5\right\}\)

hay \(n\in\left\{2;0;6\right\}\)