\(A=2+2^2+2^3+....+2^{60}=\left(2+2^2\right)+\left(2^3+2^4\right)+.....+\left(2^{59}+2^{60}\right)=1.6+2^3.\left(2+2^2\right)+....+2^{59}.\left(2+2^2\right)=1.6+2^3.6+...+2^{59}.6=\left(1+2^3+...+2^{59}\right).6=>A⋮6⋮3\)
-------------------------------------------------\(A=2+2^2+2^3+.....+2^{60}=\left(2+2^2+2^3\right)+\left(2^4+2^5+2^6\right)+.....+\left(2^{58}+2^{59}+2^{60}\right)=1.14+2^4.\left(2+2^2+2^3\right)+...+2^{58}.\left(2+2^2+2^3\right)=1.14+2^4.14+....+2^{58}.14=\left(1+2^4+...+2^{58}\right).14=>A⋮14⋮7\)
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\(A=2+2^2+2^3+...+2^{60}=\left(2+2^2+2^3+2^4\right)+\left(2^5+2^6+2^7+2^8\right)+.....+\left(2^{57}+2^{58}+2^{59}+2^{60}\right)=1.30+2^5.\left(2+2^2+2^3+2^4\right)+......+2^{57}.\left(2+2^2+2^3+2^4\right)=1.30+2^5.30+....+2^{57}.30=\left(1+2^5+...+2^{57}\right).30=>A⋮30⋮5\)
