Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
23\,\, \vdots \,\,23 \Rightarrow 23.\left( {a + b} \right)\,\, \vdots \,\,23 \Leftrightarrow \left( {23a + 23b} \right)\,\, \vdots \,\,23\\
\left( {7a + 3b} \right)\,\, \vdots \,\,23\\
\Rightarrow \left[ {\left( {23a + 23b} \right) - \left( {7a + 3b} \right)} \right]\,\, \vdots \,\,23\\
\Leftrightarrow \left[ {\left( {23a - 7a} \right) + \left( {23b - 3b} \right)} \right]\,\, \vdots \,\,23\\
\Leftrightarrow \left( {16a + 20b} \right)\,\, \vdots \,\,23\\
\Leftrightarrow \left[ {4.\left( {4a + 5b} \right)} \right]\,\, \vdots \,\,23\\
\Rightarrow \left( {4a + 5b} \right)\,\, \vdots \,\,23
\end{array}\)
Vậy \(4a + 5b\) chia hết cho 23.
