Ta có:
4n - 5
= 4n - 2 - 3
= 2(2n - 1) - 3
4n - 5 \(⋮\) 2n - 1
=> 2(2n - 1) \(⋮\) 2n - 1
=> 3 \(⋮\) 2n - 1 hay 2n - 1 \(\in\) Ư(3)
Ư(3) = \(\left\{1;-1;3;-3\right\}\)
Với 2n - 1 = 1 => 2n = 1 + 1 = 2 => n = 2 : 2 = 1
Với 2n - 1 = -1 => 2n = (-1) + 1 = 0 => n = 0 : 2 = 0
Với 2n - 1 = 3 => 2n = 3 + 1 = 4 => n = 4 : 2 = 2
Với 2n - 1 = -3 => 2n = (-3) + 1 = -2 => (-2) : 2 = -1
Vì n \(\in\) N nên n = \(\left\{0;1;2\right\}\)
\(\left(4n-5\right)⋮\left(2n-1\right)\)
=> \(\left(2.2n-1+4\right)⋮\left(2n-1\right)\)
=> \(\left(2.4+2n-1\right)⋮\left(2n-1\right)\)
=> \(\left[8+\left(2n-1\right)\right]⋮\left(2n-1\right)\)
mà \(\left(2n-1\right)⋮\left(2n-1\right)\)
=> \(8⋮\left(2n-1\right)\)
=> \(2n-1\in\left\{1;2;4;8\right\}\)
=> \(2n\in\left\{2;3;5;9\right\}\)
=> \(n\in\left\{1\right\}\)
* . Mình có cảm giác là sai sai
