17:
a: A=7^4(7^2+7-1)=7^4*55 chia hết cho 11
b: \(=3^{28}-3^{27}-3^{26}=3^{26}\left(3^2-3-1\right)=5\cdot3^2\cdot3^{24}⋮45\)
4: \(=3^n\cdot9+3^n-2^n\cdot4-2^n\)
=3^n*10-2^n*5
\(=10\left(3^n-2^{n-1}\right)⋮10\)
5:
\(=10^{98}\left(10^2+10+1\right)=111\cdot10^{98}⋮111\cdot2=222\)
6:
\(=3^n\left(27+3\right)+2^n\left(2^3+2^2\right)=3^n\cdot6\cdot5+2^n\cdot6\cdot2⋮6\)
7:
\(=4\left(1+4\right)+4^3\left(1+4\right)+...+4^{2007}\left(1+4\right)\)
=5(4+4^3+...+4^2007) chia hết cho 5
8:
Đặt \(B=4^{2007}+4^{2006}+...+4^2+4+1\)
=>4B=4^2008+4^2007+...+4^3+4^2+4
=>3B=4^2008-1
=>B=(4^2008-1)/3
\(A=75\cdot\dfrac{4^{2008}-1}{3}+25\)
=25*4^2008
=4^2007*100 chia hết cho 100
