Aratati ca 6 la puterea 2018 poate fi scris ca suma a trei cubui perfecte.

Răspuns :

6^2018=6² * 6^2016=36* (6^672)³=(1+8+27) *(6^672)³=(1+2³+3³)*(6^672)³=

(6^672)³ +(2*6^672)³+(3*6^672)³=a³+b³+c³, suma de 3 cuburi perfecte
C.C.T.D.
6^2018=6²*6^2016=36*(6^672)³=(1+8+27)*(6^672)³=(1+2³+3³)*(6^672)³=(6^672)³+(2*6^672)³+(3*6^672)³