@Dao Trong Luan , you are wrong :v 

\(A=1+2+2^2+..........+2^{14}\)

\(A=\left(2^0+2^1+2^2+2^3+2^4\right)+\left(2^5+2^6+......+2^9\right)+\left(2^{10}+2^{11}+......+2^{14}\right)\)

\(A=31.1+2^5.31+2^{10}.31\)

\(A=31\left(1+2^5+2^{10}\right)⋮31\)

1 + 2 + 2² + ... + 2¹⁴

= [1 + 2 + 2² + 2³ + 2⁴] + 2⁶[1 + 2 + 2² + 2³ + 2⁴] + 2¹¹[1 + 2 + 2² + 2³]

= 31 + 2⁶.31 + 2¹¹.15 

But 2¹¹.15 \(⋮̸31\)

=> A \(⋮̸31\)

This question was wrong