USING MAPLE

Consider the ring $R=\frac{Z}{m}Z,$ where the modulus $m=8332$ is a composite number

$[>m$:$=8332$ :

ifactor $(m)$;

Use Eulers's Theorem and the Proposition $2$ in Lecture $6$ to calculate the order $e$ of the following elements in $\frac{Z}{m}Z,$ if the order exists,

or explain why the order for the given element does not exist.

$($A$)333$

$($B$)512$

$($C$)7883$

NOTE: finding the order by the method of direct calculations$/$programming is NOT what is asked.