Question

B=2+2²+2³+2^{4_{+..............+}}2^59₊2⁶⁰ b chia hết cho 2,3,7,15

Answer 1

\(B=2\left(1+2+2^2+...+2^{58}+2^{59}\right)⋮2\)

\(B=2\left(1+2\right)+2^3\left(1+2\right)+...+2^{59}\left(1+2\right)\)

\(=3\left(2+2^3+...+2^{59}\right)⋮3\)

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

\(=7\left(2+2^4+...+2^{58}\right)⋮7\)

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

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