Question

Tim so tu nhien n sao cho:

a) 4n-5 chia het cho 2n-1

b) 6n+9 chia het cho 3n+1

 

Answer 1

\(4n-5⋮2n-1\)

\(\Leftrightarrow4n-2-3⋮2n-1\)

\(\Leftrightarrow2\left(2n-1\right)-3⋮2n-1\)

\(\Leftrightarrow-3⋮2n-1\)

\(\Leftrightarrow2n-1\in\text{Ư}\left(-3\right)=\left\{-3;-1;1;3\right\}\)

\(\Leftrightarrow2n\in\left\{-2;0;2;4\right\}\)

\(\Leftrightarrow n\in\left\{-1;0;1;2\right\}\)

mà \(n\in N\)

\(\Rightarrow n\in\left\{0;1;2\right\}\)

\(6n+9⋮3n+1\)

\(\Leftrightarrow6n+2+7⋮3n+1\)

\(\Leftrightarrow2\left(3n+1\right)+7⋮3n+1\)

\(\Leftrightarrow7⋮3n+1\)

\(\Leftrightarrow3n+1\in\text{Ư}\left(7\right)=\left\{-7;-1;1;7\right\}\)

\(\Leftrightarrow3n\in\left\{-8;-2;0;6\right\}\)

\(\Leftrightarrow n\in\left\{-\frac{8}{3};-\frac{2}{3};0;2\right\}\)

mà \(n\in N\)

=> \(n\in\left\{0;2\right\}\)