\[\boxed{\text{1004.}\text{\ }еуроки - ответы\ на\ пятёрку}\]
\[\textbf{а)}\ 41³ + 19³ =\]
\[= (41 + 19)\]
\[\left( 41^{2} - 41 \cdot 19 + 19^{2} \right) =\]
\[= 60 \cdot \left( 41^{2} - 41 \cdot 19 + 19^{2} \right) \Longrightarrow\]
\[\Longrightarrow делится\ на\ 60.\]
\[\textbf{б)}\ 79³ - 29^{3} =\]
\[= (79 - 29)\]
\[\left( 79^{2} + 79 \cdot 29 + 29^{2} \right) =\]
\[= 50 \cdot \left( 79^{2} + 79 \cdot 29 + 29^{2} \right) \Longrightarrow\]
\[\Longrightarrow делится\ на\ 50.\]
\[\textbf{в)}\ 66³ + 34³ =\]
\[= (66 + 34)\]
\[\left( 66^{2} - 66 \cdot 34 + 34^{2} \right) =\]
\[= 100 \cdot \left( 66^{2} - 66 \cdot 34 + 34^{2} \right) =\]
\[= 100 \cdot\]
\[\cdot \left( 4 \cdot 33^{2} - 4 \cdot 17 \cdot 33 + 4 \cdot 17 \right) =\]
\[= 400 \cdot \left( 33^{2} - 17 \cdot 33 + 17 \right) \Longrightarrow\]
\[\Longrightarrow делится\ на\ 400.\]
\[\textbf{г)}\ 54³ - 24^{3} =\]
\[= (54 - 24)\]
\[\left( 54^{2} + 54 \cdot 24 + 24^{2} \right) =\]
\[= 30 \cdot\]
\[\cdot \left( 36 \cdot 9^{2} + 36 \cdot 4 \cdot 9 + 36 \cdot 4^{2} \right) =\]
\[= 1080 \cdot \left( 9^{2} + 4 \cdot 9 + 4^{2} \right) -\]
\[делится\ на\ 1080.\]