Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
{a^3} + {b^3} - {c^3}\\
= \left( {{a^3} + 3{a^2}b + 3a{b^2} + {b^3}} \right) - {c^3} - \left( {3{a^2}b + 3a{b^2}} \right)\\
= {\left( {a + b} \right)^3} - {c^3} - 3ab\left( {a + b} \right)\\
= \left( {a + b - c} \right)\left[ {{{\left( {a + b} \right)}^2} + \left( {a + b} \right).c + {c^2}} \right] - 3ab.\left( {a + b} \right)\\
= 2019.\left[ {{{\left( {a + b} \right)}^2} + \left( {a + b} \right).c + {c^2}} \right] - 3ab.\left( {a + b} \right)\\
2019 \vdots 3 \Rightarrow 2019.\left[ {{{\left( {a + b} \right)}^2} + \left( {a + b} \right).c + {c^2}} \right] \vdots 3\\
3ab\left( {a + b} \right) \vdots 3\\
\Rightarrow 2019.\left[ {{{\left( {a + b} \right)}^2} + \left( {a + b} \right).c + {c^2}} \right] - 3ab.\left( {a + b} \right) \vdots 3\\
\Leftrightarrow \left( {{a^3} + {b^3} - {c^3}} \right) \vdots 3
\end{array}\)
