Giải thích các bước giải:
Ta có:
\[\begin{array}{l}
\left( {ab + 1} \right) \vdots c\\
\left( {bc + 1} \right) \vdots a\\
\left( {ca + 1} \right) \vdots b\\
\Rightarrow \left( {ab + 1} \right)\left( {bc + 1} \right)\left( {ca + 1} \right) \vdots \left( {abc} \right)\\
\Leftrightarrow \left( {a{b^2}c + ab + bc + 1} \right)\left( {ca + 1} \right) \vdots \left( {abc} \right)\\
\Leftrightarrow \left( {a{b^2}c\left( {ac + 1} \right) + {a^2}bc + ab + ab{c^2} + bc + ca + 1} \right) \vdots abc\\
\Leftrightarrow \left( {abc\left( {abc + b + a + c} \right) + ab + bc + ca + 1} \right) \vdots abc\\
abc\left( {abc + a + b + c} \right) \vdots abc\\
\Rightarrow ab + bc + ca + 1 \vdots abc
\end{array}\]
