Question

Tìm số tự nhiên n sao cho

a) 7n chia hết cho n - 1

b) n +5 chia hết cho n +1

c) n² chia hết cho n + 3

Answer 1

a: \(\Leftrightarrow7n-7+7⋮n-1\)

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

hay \(n\in\left\{2;0;8;-6\right\}\)

b: \(\Leftrightarrow n+1+4⋮n+1\)

\(\Leftrightarrow n+1\in\left\{1;-1;2;-2;4;-4\right\}\)

hay \(n\in\left\{0;-2;1;-3;3;-5\right\}\)

c: \(\Leftrightarrow n^2-9+9⋮n+3\)

\(\Leftrightarrow n+3\in\left\{1;-1;3;-3;9;-9\right\}\)

hay \(n\in\left\{-2;-4;0;-6;6;-12\right\}\)