\(A=5+5^2+5^3+...+5^{20}\)
\(\Rightarrow A=\left(5+5^2\right)+\left(5^3+5^4\right)+...+\left(5^{19}+5^{20}\right)\)
\(\Rightarrow A=\left(5+25\right)+5^2.\left(5+5^2\right)+...+5^{18}.\left(5+5^2\right)\)
\(\Rightarrow A=30+5^2.30+...+5^{18}.30\)
\(\Rightarrow A=\left(1+5^2+...+5^{18}\right).30⋮30\)
\(\Rightarrow A⋮30\)
\(\Rightarrow A\) là bội của 3
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