\(S_2=2\left(1+2+2^2+2^3+2^4\right)+...+2^{96}.\left(1+2+2^2+2^3+2^4\right)\)\(S_2=2.31+....+2^{96}.31\)
\(S_2=31.\left(2+...+2^{96}\right)\)chia hết cho 31
Suy ra \(S_2\)chia hết cho 31
\(D=2^{1990}.\left(2^{10}+2^{12}\right)\)
\(D=2^{1990}.5120\)chia hết cho 5120
Vậy suy ra D chia hết cho 5120