Question

tim so tu nhien n sao cho (4 nhan n -12)chia het cho (3 nhan n +1)

Answer 1

\(4n-12⋮3n+1\)

\(\Rightarrow3\left(4n-12\right)⋮3n+1\)

\(\Rightarrow12n+4-40⋮3n+1\)

\(\Rightarrow4\left(3n+1\right)-40⋮3n+1\)

\(\Rightarrow40⋮3n+1\) (Vì \(4\left(3n+1\right)⋮3n+1\))

\(\Rightarrow3n+1\inƯ\left(40\right)=\left\{1;2;4;5;8;10;20;40\right\}\)

\(\Rightarrow3n\in\left\{0;1;3;4;7;9;19;39\right\}\)

Mà n \(\in\) N nên 3n \(⋮\) 3 \(\Rightarrow3n\in\left\{0;3;9;39\right\}\)

\(\Rightarrow n\in\left\{0;1;3;13\right\}\)