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a) Gọi ƯCLN (n + 3; n + 2) = d.
Ta thấy (n + 3) chia hết cho d; (n+2) chia hết cho d=>[(n + 3)- (n + 2)] chia hết cho d =>l chia hết cho d
Nên d = 1. Do đó n + 3 và n + 2 là hai số nguyên tố cùng nhau.
b) Gọi ƯCLN (3n+4; 3n + 7) = đ.
Ta thấy (3n + 4) chia hết cho d;(3n+7) chia hết cho d =>[(3n+7) - (3n + 4)] chia hết cho d =>3 chia hết cho d nên
d = 1 hoặc d = 3.
Mà (3n + 4) không chia hết cho 3; (3n + 7) không chia hết cho 3 nên d = 1. Ta có điều phải chứng minh.
c) Gọi ƯCLN (2n + 3; 4n + 8) = d.
Ta thấy (2n + 3) chia hết cho d ; (4n + 8) chia hết cho d => [(4n + 8) - 2.(2n +3)] chia hết cho d => 2 chia hết cho d
nên d = 1 hoặc d = 2.
Mà (2n+3) không chia hết cho 2 nên d = 1. Ta có điều phải chứng minh.
Bài 1 : \(\frac{-4}{8}=\frac{x}{-10}=\frac{-7}{y}=\frac{z}{-24}\)
* Ta có : \(\frac{-4}{8}=\frac{x}{-10}\)
\(\Rightarrow(-4)(-10)=x\cdot8\)
\(\Rightarrow x=\frac{(-4)\cdot(-10)}{8}=5\)
* Ta có : \(\frac{-4}{8}=\frac{-7}{y}\)
\(\Rightarrow-4\cdot y=(-7)\cdot8\)
\(\Rightarrow-4\cdot y=-56\)
\(\Rightarrow y=(-56):(-4)=14\)
* Ta có : \(\frac{-4}{8}=\frac{z}{-24}\)
\(\Rightarrow(-4)\cdot(-24)=z\cdot8\)
\(\Rightarrow96=z\cdot8\)
\(\Rightarrow z=96:8=12\)
Vậy : ...
P/S : Lần sau nhớ đăng 1 hay 2 bài thôi chứ nhiều quá làm sao hết
\(\frac{-4}{8}=\frac{x}{-10}=\frac{-7}{y}=\frac{z}{-24}\)
\(\text{ Ta có : }\frac{-4}{8}=\frac{-1}{2};\frac{x}{-10}=\frac{-x}{10};\frac{z}{-24}=\frac{-z}{24}\)
\(\text{+) }\frac{-1}{2}=\frac{-x}{10}\)
\(\Leftrightarrow\left(-1\right).10=2.\left(-x\right)\)
\(\Leftrightarrow-x=\frac{\left(-1\right).10}{2}\)
\(\Leftrightarrow-x=-5\)
\(\Leftrightarrow x=5\)
\(\text{+) }\frac{-1}{2}=\frac{-7}{y}\)
\(\Leftrightarrow\left(-1\right).y=2.\left(-7\right)\)
\(\Leftrightarrow y=\frac{2.\left(-7\right)}{-1}\)
\(\Leftrightarrow y=14\)
\(\text{+) }\frac{-1}{2}=\frac{-z}{24}\)
\(\Leftrightarrow\left(-1\right).24=2.\left(-z\right)\)
\(\Leftrightarrow-z=\frac{\left(-1\right).24}{2}\)
\(\Leftrightarrow-z=-12\)
\(\Leftrightarrow z=12\)
2,
+ n chẵn
=> n(n+5) chẵn
=> n(n+5) chia hết cho 2
+ n lẻ
Mà 5 lẻ
=> n+5 chẵn => chia hết cho 2
=> n(n+5) chia hết cho 2
KL: n(n+5) chia hết cho 2 vơi mọi n thuộc N
3,
A = n2+n+1 = n(n+1)+1
a,
+ Nếu n chẵn
=> n(n+1) chẵn
=> n(n+1) lẻ => ko chia hết cho 2
+ Nếu n lẻ
Mà 1 lẻ
=> n+1 chẵn
=> n(n+1) chẵn
=> n(n+1)+1 lẻ => ko chia hết cho 2
KL: A không chia hết cho 2 với mọi n thuộc N (Đpcm)
b, + Nếu n chia hết cho 5
=> n(n+1) chia hết cho 5
=> n(n+1)+1 chia 5 dư 1
+ Nếu n chia 5 dư 1
=> n+1 chia 5 dư 2
=> n(n+1) chia 5 dư 2
=> n(n+1)+1 chia 5 dư 3
+ Nếu n chia 5 dư 2
=> n+1 chia 5 dư 3
=> n(n+1) chia 5 dư 1
=> n(n+1)+1 chia 5 dư 2
+ Nếu n chia 5 dư 3
=> n+1 chia 5 dư 4
=> n(n+1) chia 5 dư 2
=> n(n+1)+1 chia 5 dư 3
+ Nếu n chia 5 dư 4
=> n+1 chia hết cho 5
=> n(n+1) chia hết cho 5
=> n(n+1)+1 chia 5 dư 1
KL: A không chia hết cho 5 với mọi n thuộc N (Đpcm)
![YTP] Huấn Hoa Hồng Chế](data:image/jpeg;base64,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)
Bài 1:
a: \(=2^{24}+2^{60}=2^{24}\left(2^{36}+1\right)\)
\(=2^{24}\left(2^4+1\right)\cdot A=17\cdot B⋮17\)
b: \(A=2\left(1+2+2^2+2^3\right)+2^5\left(1+2+2^2+2^3\right)+...+2^{57}\left(1+2+2^2+2^3\right)\)
\(=15\cdot\left(2+2^5+...+2^{57}\right)\) chia hết cho 3;5;15
\(A=2\left(1+2+2^2+...+2^{59}\right)⋮2\)
\(A=2\left(1+2+2^2\right)+2^4\left(1+2+2^2\right)+...+2^{58}\left(1+2+2^2\right)\)
\(=7\left(2+2^4+...+2^{58}\right)⋮7\)