Question: If d is a positive integer, d $\neq 2$ and d divides n, show that the number of elements of order d in $D_{n}$ is $\phi \left ( d \right )$. How many elements of order 2 does $D_{n}$ have?
Theorem: If d is a positive divisor of n, the number of elements of order d in a cyclic group of order n is $\left \langle d \right \rangle$.
$D_{n}$ has order 2n.
d is a positive integer and d divides n so there exists a subgroup, say $\left \langle a \right \rangle$, of order d.
Hints are appreciated. Thanks in advance.
