Possible Duplicate:
GCD and roots of unity
If we have some roots of unity $\zeta$ and $\rho$, in which $o(\zeta)=a$ and $o(\rho)=b$, can we prove that $o(\zeta\rho)=\operatorname{lcm}[a,b]$? If not, can we prove that this is not true?
Possible Duplicate:
GCD and roots of unity
If we have some roots of unity $\zeta$ and $\rho$, in which $o(\zeta)=a$ and $o(\rho)=b$, can we prove that $o(\zeta\rho)=\operatorname{lcm}[a,b]$? If not, can we prove that this is not true?