Question

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

Answer 1

\(\left(ab+cd+eg\right)⋮11\)

\(\Rightarrow\left(9999ab+99cd+ab+cd+eg\right)⋮11\)

\(\Rightarrow\left(10000ab+100cd+eg\right)⋮11\)

\(\Rightarrow abcdeg⋮11\left(đpcm\right)\)

Answer 2

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

\(\Rightarrow10000\overline{ab}+100\overline{cd}+\overline{eg}⋮11\)

\(\Rightarrow\overline{abcdeg}⋮11\)