Question

\(Ch\text{ứng}\)\(minh\)\(r\text{ằng}\)\(3a+2b⋮17\Leftrightarrow10a+b⋮17\)

Answer 1

Ta có :

\(3a+2b⋮17\)

\(\Rightarrow9\left(3a+2b\right)⋮17\)

\(\Rightarrow27a+18b⋮17\)

\(\Rightarrow\left(17a+17b\right)+\left(10a+b\right)⋮17\)

\(\Rightarrow10a+b⋮17\)(1)

Ta có :

\(10a+b⋮17\)

\(\Rightarrow2\left(10a+b\right)⋮17\)

\(\Rightarrow20a+2b⋮17\)

\(\Rightarrow17a+3a+2b⋮17\)

\(\Rightarrow3a+2b⋮17\)(2)

Từ (1) và (2) \(\Rightarrow3a+2b⋮17\Leftrightarrow10a+b⋮17\)(đpcm)

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