Question

Chứng minh :

Nếu \(\overline{ab}+\overline{cd}+\overline{eg}⋮11\) thì \(\overline{abcdeg}⋮11\)

Answer 1

Ta có : \(\overline{abcdeg}=10000.\overline{ab}+100.\overline{cd}+\overline{eg}\)

\(=\left(9999+1\right).\overline{ab}+\left(99+1\right).\overline{cd}+\overline{eg}\)

\(=9999.\overline{ab}+\overline{ab}+99.\overline{cd}+\overline{cd}+\overline{eg}\)

\(=11.909.\overline{ab}+ab+11.9.\overline{cd}+\overline{cd}+\overline{eg}\)

Vì \(11.909.\overline{ab}⋮11;11.9.\overline{cd}⋮11;\overline{ab}+\overline{cd}+\overline{eg}⋮11\) nên \(\overline{abcdeg}⋮11\)