1. between

2. of

3. in

4. on

5. of

6. to

7. in

8. like

9. up-at

10. in

C. drink

Ta có: \(4^{567}=4^{2.283}.4=\left(4^2\right)^{283}.4=\left(...6\right)^{283}.4=\left(...6\right).4=\left(...4\right)\)

Ta có: \(14^{14}=14^{2.7}=\left(14^2\right)^7=\left(...6\right)^7=\left(...6\right)\)

Ta có: \(7^{99}=7^{4.24}.7^3\)\(=\left(7^4\right)^{24}.\left(...3\right)=\left(...1\right)^{24}.\left(...3\right)=\left(...1\right).\left(...3\right)\)\(=\left(...3\right)\)

Ta có: \(13^{1003}=13^{4.250}.13^3\) \(=\left(13^4\right)^{250}.\left(...7\right)\) \(=\left(...1\right)^{250}.\left(..7\right)\)

\(=\left(...1\right).\left(...7\right)\) \(=\left(...7\right)\)

Ta có : \(19^{21}=19^{2.10}.19=\left(19^2\right)^{10}.19=\left(...1\right)^{10}.19\)

\(=\left(...1\right).19\)\(=\left(...9\right)\)

Ta có: \(17^{2007}\) = \(17^{4.501}.17\) = \(\left(17^4\right)^{501}.17\) = \(\left(...1\right)^{501}.17\) = \(\left(...1\right).17=...7\)

b, Để A là phân số tối giản thì (n+1;n-3) = 1

Gọi d là ƯC(n+1;n-3), \(\left(d\in N\right)\)

Ta có: \(\left\{{}\begin{matrix}n+1⋮d\\n-3⋮d\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}\left(n-3\right)+4⋮d\\n-3⋮d\end{matrix}\right.\) \(\Rightarrow4⋮d\)

\(\Rightarrow d\in\left\{1;2;4\right\}\)

Để A là phân số tối giản thì d = 1

\(\Rightarrow d\ne2và4\)

\(\Rightarrow n+1\) là số lẻ

\(\Rightarrow n\) là số chẵn và \(n\ne2;4\)

\(\Rightarrow n=2k\)(\(k\in N\))

a, Để A \(\in\) Z thì n+1\(⋮\) n-3

Ta có: \(\left\{{}\begin{matrix}n+1⋮n-3\\n-3⋮n-3\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}n+1⋮n-3\\(n+1)-4⋮n-3\end{matrix}\right.\)\(\Rightarrow4⋮n-3\)

\(\Rightarrow n-3\inƯ\left(4\right)\)

\(\Rightarrow n-3\in\left\{\pm1;\pm2;\pm4\right\}\)

\(\Rightarrow n\in\left\{-1;1;2;4;5;7\right\}\)