a) \(5^{15}+5^{14}+5^{13}\)

\(=5^{12}\left(5^3+5^2+5\right)\)

=\(5^{12}\left(125+25+5\right)\)

=\(5^{12}\times155=5^{12}\times5\times31\)chia hết cho 31

b)\(7^6+7^5+7^4\)ko chia hết cho 8 (bấm máy tính là ra)

c)\(2^{10}+2^9+2^8+2^7\)

\(=2^7\left(2^3+2^2+2+2^0\right)\)

\(=2^7\left(8+4+2+1\right)\)

\(=2^7\times15\) chia hết cho 15

a) 8⁷-2¹⁸

=(2³)⁷-2¹⁸

=2²¹-2¹⁸

=2¹⁸.(2³-1)

=2¹⁸. 7

=2¹⁷.2.7

=2¹⁷.14  chia het cho 14

81^7-27^9-9^13 
=(3^4)^7-(3^3)^9-(3^2)^13 
=3^28-3^27-3^26 
=(3^26.3^2)-(3^26.3^1)-(3^26.1) 
=3^26.(9-3-1) 
=3^22.(3^4.5) 
=3^22.405 chia het cho 405 
=> 81^7-27^9-9^13 chia het cho 405

a: \(8^8+2^{20}\)

\(=\left(2^3\right)^8+2^{20}\)

\(=2^{24}+2^{20}=2^{20}\left(2^4+1\right)=2^{20}\cdot17\) ⋮17

b: \(A=10^{28}+8=10\ldots08\) (Với 28 chữ số 0)

A có tổng các chữ số là 1+0+0+...+0+8=9

=>A⋮9

Ta có: \(10^{28}=10^3\cdot10^{25}=1000\cdot10^{25}=8\cdot125\cdot10^{25}\) ⋮8

8⋮8

Do đó: \(10^{28}+8\) ⋮8

=>A⋮8

mà A⋮9

và ƯCLN(8;9)=1

nên A⋮8*9

=>A⋮72

c: \(T=2+2^2+2^3+\cdots+2^{60}\)

\(=\left(2+2^2+2^3+2^4\right)+\left(2^5+2^6+2^7+2^8\right)+\cdots+\left(2^{57}+2^{58}+2^{59}+2^{60}\right)\)

\(=2\left(1+2+2^2+2^3\right)+2^5\left(1+2+2^2+2^3\right)+\cdots+2^{57}\left(1+2+2^2+2^3\right)\)

\(=15\left(2+2^5+\cdots+2^{57}\right)\)

=>T⋮15

mà 15⋮3

nên T⋮3

Ta có: \(T=2+2^2+2^3+\cdots+2^{60}\)

\(=\left(2+2^2+2^3\right)+\left(2^4+2^5+2^6\right)+\cdots+\left(2^{58}+2^{59}+2^{60}\right)\)

\(=2\left(1+2+2^2\right)+2^4\left(1+2+2^2\right)+\cdots+2^{58}\left(1+2+2^2\right)\)

\(=7\left(2+2^4+\cdots+2^{58}\right)\) ⋮7