How to find n elements of order o in U(m)

Question

For example, to find 4 elements of order 47 in U(187), is there a simpler way to do it instead of finding 2 more numbers except 1 and 186 by going through all possibilities from 2 to 185?

Answer 1

$187 = 11 \times 17$ so $\phi(187) = 10 \cdot 16 = 160$.

The order of the group of units $U(187)$ is thus 160.

The order of an element of $U(187)$ thus divides $160$, so no element of order $47$ can exist.