E.575. Scrieți numărul a=152018a=15^{2018}a=152018 ca sumă de 555 cuburi perfecte.
Răspuns: a=(5⋅15672)3+(4⋅15672)3+(3⋅15672)3+(2⋅15672)3+(15672)3.a=(5 \cdot 15^{672})^3 + (4 \cdot 15^{672})^3 + (3 \cdot 15^{672})^3 + (2 \cdot 15^{672})^3 + (15^{672})^3.a=(5⋅15672)3+(4⋅15672)3+(3⋅15672)3+(2⋅15672)3+(15672)3.
a=152⋅152016=a=15^2 \cdot 15^{2016}=a=152⋅152016= =(53+43+33+23+13)⋅(15672)3==(5^3+4^3+3^3+2^3+1^3) \cdot (15^{672})^3==(53+43+33+23+13)⋅(15672)3= =(5⋅15672)3+(4⋅15672)3+(3⋅15672)3+(2⋅15672)3+(15672)3.=(5 \cdot 15^{672})^3 + (4 \cdot 15^{672})^3 + (3 \cdot 15^{672})^3 + (2 \cdot 15^{672})^3 + (15^{672})^3.=(5⋅15672)3+(4⋅15672)3+(3⋅15672)3+(2⋅15672)3+(15672)3.