a, Ta có:12=22.3
18=2.32
=>ƯCLN(12;18)=2.3=6
b, \(A=1+4+4^2+4^3+...+4^{2021}\)
=>\(A=\left(1+4+4^2\right)+\left(4^3+4^4+4^5\right)+...+\left(4^{2019}+4^{2020}+4^{2021}\right)\)
=>\(A=1.21+4^3.\left(1+4+4^2\right)+....+4^{2019}.\left(1+4+4^2\right)+\)
=>\(A=1.21+4^3.21+...+4^{2019}.21\)
=>\(A=\left(1+4^3+...+4^{2019}\right).21\)
=>A⋮21