\(A=2\left(2+1\right)+2^3\left(2+1\right)+...+2^{59}\left(2+1\right)\)
\(=3\cdot\left(2+2^3+...+2^{59}\right)⋮3\)
\(A=\left(2+2^2\right)+\left(2^3+2^4\right)+...+\left(2^{59}+2^{60}\right)\\ A=2\left(1+2\right)+2^3\left(1+2\right)+...+2^{59}\left(1+2\right)\\ A=\left(1+2\right)\left(2+2^3+...+2^{59}\right)\\ A=3\left(2+2^3+...+2^{59}\right)⋮3\\ A=\left(2+2^2+2^3\right)+\left(2^4+2^5+2^6\right)+...+\left(2^{58}+2^{59}+2^{60}\right)\\ A=2\left(1+2+2^2\right)+2^4\left(1+2+2^2\right)+...+2^{58}\left(1+2+2^2\right)\\ A=\left(1+2+2^2\right)\left(1+2^4+...+2^{58}\right)\\ A=7\left(1+2^4+...+2^{58}\right)⋮7\)
