Question Number 46083 by peter frank last updated on 20/Oct/18
Answered by tanmay.chaudhury50@gmail.com last updated on 21/Oct/18
$$\alpha^{\mathrm{7}} =\mathrm{1} \\ $$$$\alpha^{\mathrm{7}} −\mathrm{1}=\mathrm{0} \\ $$$$\left(\alpha−\mathrm{1}\right)\left(\alpha^{\mathrm{6}} +\alpha^{\mathrm{5}} +\alpha^{\mathrm{4}} +\alpha^{\mathrm{3}} +\alpha^{\mathrm{2}} +\alpha+\mathrm{1}\right)=\mathrm{0} \\ $$$$ \\ $$$${when}\:{A}×{B}=\mathrm{0} \\ $$$${either}\:{A}=\mathrm{0}\:{or}\:{B}=\mathrm{0} \\ $$$${hence}\:\alpha^{\mathrm{6}} +\alpha^{\mathrm{5}} +\alpha^{\mathrm{4}} +\alpha^{\mathrm{3}} +\alpha^{\mathrm{2}} +\alpha+\mathrm{1}=\mathrm{0} \\ $$
Commented by peter frank last updated on 21/Oct/18
$$\mathrm{thanks} \\ $$