Question

Chứng minh rằng nếu : ( ab + cd + eg )chia hết cho 11 thì abcdeg chia hết cho 11

giúp mk với

Answer 1

Ta có: \(\overline{abcdeg}=\overline{ab0000}+\overline{cd00}+\overline{eg}\)

\(=\overline{ab}.10000+\overline{cd}.100+\overline{eg}\)

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

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

\(=11.\left(\overline{ab}.909+\overline{cd}.99\right)+\left(\overline{ab}+\overline{cd}+\overline{eg}\right)\)

Vì \(11.\left(\overline{ab}.909+\overline{cd}.99\right)⋮11\) và \(\overline{ab}+\overline{cd}+\overline{eg}⋮11\) nên \(\overline{abcdeg}⋮11\) (đpcm)