\(A=2+2^2+2^3+\cdots+2^{60}\)
\(=\left(2+2^2+2^3+2^4+2^5+2^6\right)+\left(2^7+2^8+2^9+2^{10}+2^{11}+2^{12}\right)+\cdots+\left(2^{55}+2^{56}+2^{57}+2^{58}+2^{59}+2^{60}\right)\)
\(=2\left(1+2+2^2+2^3+2^4+2^5\right)+2^7\left(1+2+2^2+2^3+2^4+2^5\right)+\cdots+2^{55}\left(1+2+2^2+2^3+2^4+2^5\right)\)
\(=63\left(2+2^7+\cdots+2^{55}\right)\) ⋮21
\(A=2+2^2+2^3+\cdots+2^{60}\)
\(=\left(2+2^2+2^3+2^4\right)+\left(2^5+2^6+2^7+2^8\right)+\cdots+\left(2^{57}+2^{58}+2^{59}+2^{60}\right)\)
\(=2\left(1+2+2^2+2^3\right)+2^5\left(1+2+2^2+2^3\right)+\cdots+2^{57}\left(1+2+2^2+2^3\right)\)
\(=15\left(2+2^5+\cdots+2^{57}\right)\) ⋮15
