\(C=1+4+4^2+...+4^{20}\)
\(C=\left(1+4\right)+4^2\left(1+4\right)+4^4\left(1+4\right)+...+4^{18}\left(1+4\right)\)
\(C=5\left(1+4^2+4^4+...+4^{18}\right)⋮5\)
\(C=1+4+4^2+...+4^{19}\)
\(C=\left(1+4+4^2+4^3\right)+4^4\left(1+4+4^2+4^3\right)+...+4^{16}\left(1+4+4^2+4^3\right)\)\(C=85\left(1+4^4+...+4^{16}\right)\)
Nhớ tick
\(C=\left(1+4\right)+\left(4^2+4^3\right)+...+\left(4^{18}+4^{19}\right)\)
\(=5+4^2\left(1+4\right)+4^4\left(1+4\right)+...+4^{18}\left(1+4\right)\)
\(=5+5.4^2+5.4^4+...+5.4^{18}\)
\(\Rightarrow C⋮5\)
\(C=\left(1+4^2\right)+\left(4+4^3\right)+...+\left(4^{17}+4^{19}\right)\)
\(C=\left(1+4^2\right)+4\left(1+4^2\right)+...+4^{17}\left(1+4^2\right)\)
\(C=17+4.17+...+4^{17}.17\)
\(\Rightarrow C⋮17\)
Mà 5 và 17 nguyên tố cùng nhau \(\Rightarrow C⋮\left(5.17\right)\Rightarrow C⋮85\)