1)  \(B=1+5+5^2+5^3+....+5^{101}\)

\(=\left(1+5\right)+\left(5^2+5^3\right)+.....+\left(5^{100}+5^{101}\right)\)

\(=\left(1+5\right)+5^2\left(1+5\right)+....+5^{100}\left(1+5\right)\)

\(=\left(1+5\right)\left(1+5^2+....+5^{100}\right)\)

\(=6\left(1+5^2+...+5^{100}\right)\)\(⋮6\)

2)  \(C=81^3+3^{14}+27^5\)

\(=\left(3^4\right)^3+3^{14}+\left(3^3\right)^5\)

\(=3^{12}+3^{14}+3^{15}\)

\(=3^{12}.\left(1+3^2+3^3\right)\)

\(=3^{12}.37\)\(⋮37\)

Ư(720) { 1 ; 2 ; 4 ; 5 ; 6 ; ..........}

Ư(540) { 1 ; 2 ; 4 ; 5 ; 6 ; ............}

Theo bài ra,ta có:

720 : a

540 : a

\(\Rightarrow\)a \(\in\)Ư { 720 ; 540 }

720 = \(2^4\). 3\(^2\).5

540 = \(2^2\).\(3^2\). 5

ƯCLN ( 720;540 ) = 2\(^2\).\(3^2\).5 = 180

ƯC ( 720;540 ) = { 1;;2;3;4;5;6;9;10;18;12;15;90;;60;36;45;30;20;180}

Mà 75 < a <98

Nên a = 90

taco 20x34y chia hết cho 2,5​

y=0

mà 20x34ychia hết cho 3,9

tong các chữ số cua 20x340 la

2+0+x+3+4+0=9+x

suy ra x=0 , 3,6 ,9

Ta có (x-2)^4=4096

suy ra:x-2=8

x=8+2

x=10

( x - 2 ) \(^4\)=4096

=> ( x-2 ) \(^4\)=2\(^{12}\)

=> ( x-2 ) \(^4\)=( 2\(^3\))\(^4\)

=> ( x - 2 ) \(^4\)= 8\(^4\)

=> x - 2 = 8 

          x = 8+2

          x = 10