Prove that if: a = x+ y b=xw+yw² c=xw²+yw^4 ,
Than abc = x³+y³ and a²+b²+c²=6xy
i guess that w is a root of unity of w^3=1 then, 1+w+w^2=0
abc=(x+y)(xw+yw^2)(xw^2+yw^4)
=(x+y)(x^2w^3+xyw^5+xyw^4+y^2w^6)
=(x+y)(x^2+xy(w^2+w)+y^2)
=(x+y)(x^2-xy+y^2)=x^3+y^3
a^2+b^2+c^2=(a+b+c)^2-2(ab+bc+ca)