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\(a,\Rightarrow n-2+5⋮n-2\\ \Rightarrow n-2\inƯ\left(5\right)=\left\{-5;-1;1;5\right\}\\ \Rightarrow n\in\left\{-3;1;3;7\right\}\\ b,\Rightarrow2\left(n-4\right)+13⋮n-4\\ \Rightarrow n-4\inƯ\left(13\right)=\left\{-13;-1;1;13\right\}\\ \Rightarrow n\in\left\{-9;3;5;17\right\}\\ c,\Rightarrow6n-9⋮3n+1\\ \Rightarrow2\left(3n+1\right)-12⋮3n+1\\ \Rightarrow3n+1\inƯ\left(12\right)=\left\{-12;-6;-4;-3;-2;-1;1;2;3;4;6;12\right\}\\ \Rightarrow n\in\left\{-1;0;1\right\}\left(n\in Z\right)\\ d,\Rightarrow n^2+2n-n-2+3⋮n+2\\ \Rightarrow n\left(n+2\right)-\left(n+2\right)+3⋮n+2\\ \Rightarrow n+2\inƯ\left(3\right)=\left\{-3;-1;1;3\right\}\\ \Rightarrow n\in\left\{-5;-3;-1;1\right\}\)
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a: \(\Leftrightarrow n-2\in\left\{1;-1;5;-5\right\}\)
hay \(n\in\left\{3;1;7;-3\right\}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
https://loga.vn/hoi-dap/tim-so-tu-nhien-n-sao-cho-n-6-chia-het-cho-n-2-36137
https://h7.net/hoi-dap/toan-6/tim-so-tu-nhien-n-de-3n-7-chia-het-cho-n-faq26687.html
n(2n-3)-2n(n+2)
=2n2-3n-2n2-4n
= - 7n luôn chia hết cho 7 (vì -7 chia hết cho 7)
vậy n(2n-3)-2n(n+2) luôn chia hết cho 7 với mọi n
tham khảo ở link bn nhé
a) Ta có: 6 ⋮ 𝑛 => n \(\in\)Ư(6) = {1; 2; 3; 6}
b) 6 ⋮ (n - 1) => n - 1 \(\in\)Ư(6) = {1; 2; 3; 6}
Với n - 1 = 1 => n = 2
n - 1 = 2 => n = 3
n - 1 = 3 => n = 4
n - 1 = 6 => n = 7
c) Ta có: (n + 5) ⋮ n
=> 5 ⋮ n (vì n ⋮ n)
=> n \(\in\)Ư(5) = {1; 5}
d) Ta có: (n + 4) ⋮ (n + 1)
<=> (n + 1 + 3) ⋮(n + 1)
<=> 3⋮(n + 1) (vì (n + 1) ⋮( n + 1)
<=> n + 1 \(\in\)Ư(3) = {1; 3}
Với n + 1 = 1 => n = 0
n + 1 = 3 => n = 2