Question

a) (8⁸ + 8²⁰⁾ ⋮ 17

b) A= 2 + 2² + 2³ + 2⁴ + ....... + 2⁶⁰ ⋮ 2,3,7,15

Answer 1

a: \(=\left(2^{24}+2^{60}\right)\)

\(=2^{24}\left(2^{36}+1\right)\)

\(=2^{24}\cdot\left(2^4+1\right)\cdot A=17\cdot B⋮17\)

b: \(A=2\left(1+2+2^2\right)+2^4\left(1+2+2^2\right)+...+2^{58}\left(1+2+2^2\right)\)

\(=7\left(2+2^4+...+2^{58}\right)⋮7\)

\(B=2\left(1+2+2^2+2^3\right)+...+2^{57}\left(1+2+2^2+2^3\right)\)

=15(2+...+2^57) chia hết cho 3;15

=30(1+...+2^56) chia hết cho 2