Question

chứng tỏ rằng

a) (8⁸ + 8²⁰) ⋮ 17

b) A = 2 + 2² + 2³ + 2⁴ + 2⁵ +........+ 2⁶⁰ ⋮ 2,3,5,7,15

Answer 1

a: \(=2^{24}+2^{60}=2^{24}\left(1+2^{36}\right)\)

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

b: \(A=2\left(1+2+2^2+2^3\right)+2^5\left(1+2+2^2+2^3\right)+...+2^{57}\left(1+2+2^2+2^3\right)\)

\(=15\left(2+2^5+...+2^{57}\right)\) chia hết cho 3;5;15

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

\(=7\left(2+2^4+...+2^{58}\right)⋮7\)