Ta có : \(A=5+5^2+5^3+...+5^{48}\)
\(=\left(5+5^2+5^3\right)+...+\left(5^{46}+5^{47}+5^{48}\right)\)
\(=5\cdot\left(1+5+5^2\right)+...+5^{46}\cdot\left(1+5+5^2\right)\)
\(=5\cdot31+...+5^{46}\cdot31\)
\(=31\cdot\left(5+...+5^{46}\right)\) chia hết cho 31
lại có : \(A=5+5^2+5^3+5^4+...+5^{48}\)
\(=\left(5+5^2+5^3+5^4\right)+...+\left(5^{45}+5^{46}+5^{47}+5^{48}\right)\)
\(=5\cdot\left(1+5+5^2+5^3\right)+...+5^{45}\cdot\left(1+5+5^2+5^3\right)\)
\(=5\cdot156+...+5^{45}\cdot156\)
\(=156\cdot\left(5+..+5^{45}\right)\) chia hết cho 156
Ta thấy : A chia hết cho 31
A chia hết cho 156 => A chia hết cho 156 . 31
=> A chia hết cho 4836 ( đpcm)
