I am in dire need of help! $\displaystyle U_n$ is an abelian group under multiplication mod $\displaystyle (n)$. If you need more information, please let me know.

1) Find an element of maximal order in $\displaystyle U_{884}$.

2) Let $\displaystyle a$ and $\displaystyle e$ be integers with $\displaystyle e \geq4$ and $\displaystyle |[a]_{16}|=4$. Prove that $\displaystyle |[a]_{2^e}|= 2^{e-2}$

3) Let $\displaystyle e$ and $\displaystyle f$ be positive integers.

(a) Determine the number of elements of order $\displaystyle 2^f$ in $\displaystyle U_{2^e}$.

(b) Compute $\displaystyle |\{a^{2^f} | a\in U_{2^e}\}| $

Thanks for any and all help! I need help with these by tomorrow night, thanks