Question

Cho A = \(51^n+47^{102}\) (n \(\in\) N) . Chứng minh A chia hết cho 10

Answer 1

Ta có:

\(A=51^n+47^{102}\)

\(\Rightarrow A=\overline{...1}+47^{100}.47^2\)

\(\Rightarrow A=\overline{...1}+\left(47^4\right)^{25}.\left(\overline{...9}\right)\)

\(\Rightarrow A=\overline{...1}+\left(\overline{...1}\right)^{25}.\left(\overline{...9}\right)\)

\(\Rightarrow A=\overline{...1}+\left(\overline{...1}\right).\left(\overline{...9}\right)\)

\(\Rightarrow A=\overline{...1}+\overline{...9}\)

\(\Rightarrow A=\overline{...0}\)

Vì \(\overline{....0}\text{⋮}10\) nên \(A\text{⋮}10\)

Vậy \(A\text{⋮}10\left(đpcm\right)\)