Question

se scrie numarul a= 15 la puterea 2018 ca suma de cinci cuburi perfecte

Answer 1

$a=15^{2018}\\ \\ a=15 \cdot 15 \cdot 15^{2016}\\ \\ a=225 \cdot 15^{2016}\\ \\ a=(1+8+27+64+125)\cdot 15^{2016}\\ \\ a=(1^{3}+2^{3}+3^{3}+4^{3}+5^{3})\cdot (15^{672})^{3}\\ \\ a=1^{3}\cdot(15^{672})^{3}+2^{3}\cdot(15^{672})^{3}+3^{3}\cdot(15^{672})^{3}+4^{3}\cdot(15^{672})^{3}+5^{3}\cdot(15^{672})^{3}\\ \\ a=(1\cdot15^{672})^{3}+(2\cdot15^{672})^{3}+(3\cdot15^{672})^{3}+(4\cdot15^{672})^{3}+(5\cdot15^{672})^{3}$