41. All natural numbers less than $p^{3}$, where $p$ is a prime number, are considered. How many of these numbers are coprime with the number $p^{3}$?
41. Among the first $p^{3}$ natural numbers, there are $\mathrm{p}^{3}: \mathrm{p}=\mathrm{p}^{2}$ numbers that are multiples of $p$ (including $p^{3}$). Since $p$ is a prime number, the remaining $p^{3}-p^{2}$ numbers will be less than $p^{3}$ and coprime with $p$.