Question

Scrieti nr 6 la puterea 2015 ca o suma  de trei cuburi perfecte nenule.

Answer 1

$6^{2015}$=$6^{3*671+2}$=36*$( 6^{671} )^3$

Scriem pe 36 ca suma de trei cuburi perfecte nenule:

36=1+8+27=$1^{3} + 2^{3} + 3^{3}$, deci:

$6^{2015}$=$( 6^{671} )^3$($1^{3} + 2^{3} + 3^{3}$), de unde:

$6^{2015}$=$( 6^{671} )^{3} * 1^{3} + ( 6^{671} )^{3} * 2^{3} + ( 6^{671} )^{3} * 3^{3}$, adica:

$6^{2015}$=$( 6^{671} *1)^{3} + ( 6^{671} *2)^{3} + ( 6^{671} *3)^{3}$