$\\$
Sửa đề :
`A = 2+2^2+...+2^{2003}+2^{2004}`
`->A=(2+2^2+2^3+2^4+2^5)+...+(2^{2000}+2^{2001}+2^{2002}+2^{2003}+2^{2004})`
`->A = (2 . 1 + 2 . 2 +2 . 2^2 + 2 . 2^3 + 2 . 2^4)+...+(2^{2000} . 1 +2^{2000} . 2 +2^{2000}.2^2 +2^{2000} . 2^3+2^{2000} . 2^4)`
`-> A = 2 . (1+2+2^2 +2^3 +2^4)+...+2^{2000} . (1+2+2^2+2^3+2^4)`
`-> A = 2 . (1+2+4+8+16) + ... + 2^{2000} . (1+2+4+8+16)`
`->A=2 . 31 + ... + 2^{2000} . 31`
`->A = 31 . (2+...+2^{2000})`
Vì `31` chia hết cho `31`
`->31 . (2+...+2^{2000})` chia hết cho `31`
`-> A` chia hết cho `31` (đpcm)
