If $\displaystyle L = \frac{3+\sqrt{-3}}{2}$, and if $x\equiv 1\pmod{L}$,
show that $x^3\equiv 1\pmod{L^4}$.
I have already shown that if $x\equiv 1\pmod{L}$,
then $x^3\equiv 1\pmod{L^3}$.
Thanks.
If $\displaystyle L = \frac{3+\sqrt{-3}}{2}$, and if $x\equiv 1\pmod{L}$,
show that $x^3\equiv 1\pmod{L^4}$.
I have already shown that if $x\equiv 1\pmod{L}$,
then $x^3\equiv 1\pmod{L^3}$.
Thanks.