\(A=\left(2^0+2^1+2^2\right)+\left(2^3+2^4+2^5\right)+....+\left(2^{2010}+2^{2011}+2^{2012}\right)\)
\(A=\left(1+2+4\right)+2^3\left(1+2+4\right)+....+2^{2010}\left(1+2+4\right)\)
\(A=7+7.2^3+....+7.2^{2010}\)
\(A=7.\left(1+2^3+2^{2010}\right)\) chia hết cho 7.
Vậy A chia 7 dư 0