Hi there
I've got the following exercise to solve:

One sends the $\displaystyle d=p^3 \in \mathbb{Z}_{2038074743}$. You catch up $\displaystyle d=1933360524$. Calculate p now.

With $\displaystyle k:=2038074743$ I have by Euclid $\displaystyle 1=679358248*3k$ so as far as I know $\displaystyle c^{679358248}=p$ in $\displaystyle \mathbb{Z}_k$
I calculated this a couple of times now. I get p=709704058 but $\displaystyle p^3 \text{ MOD } k $ is not d.
Where is my fault?
Regards