\(S=4+4^2+4^3+...+4^{2004}\\=2^2+2^4+2^6+...+2^{4008}\\ =\left(2^2+2^4\right)+\left(2^6+2^8\right)+...+\left(2^{2002}+2^{2004}\right)\\ =2.\left(2+8\right)+2^5.\left(2+8\right)+...+2^{2001}.\left(2+8\right)\\ =2.10+2^5.10+...+2^{2001}.10 \)
Vì 10 nhân với bao nhiêu cung chia hết cho 10.
=>\(S⋮10\)