Question

Tìm n thuộc N:

a/ 2n + 3 chia hết cho n + 1

b/ 3n + 5 chia hết cho n - 1

c/ 4n + 10 chia hết cho 2n + 3

d/ 5n + 6 chia hết cho 3n + 1

Answer 1

a: \(\Leftrightarrow2n+2+1⋮n+1\)

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

hay \(n\in\left\{0;-2\right\}\)

b: \(\Leftrightarrow3n-3+8⋮n-1\)

\(\Leftrightarrow n-1\in\left\{1;-1;2;-2;4;-4;8;-8\right\}\)

hay \(n\in\left\{2;0;3;-1;5;-3;9;-7\right\}\)

c: \(\Leftrightarrow4n+6+4⋮2n+3\)

\(\Leftrightarrow2n+3\in\left\{1;-1\right\}\)

hay \(n\in\left\{-1;-2\right\}\)

d: \(\Leftrightarrow15n+18⋮3n+1\)

\(\Leftrightarrow15n+5+13⋮3n+1\)

\(\Leftrightarrow3n+1\in\left\{1;-1;13;-13\right\}\)

hay \(n\in\left\{0;4\right\}\)