# How to find the elements of a specific order in a cyclic group

I have a cyclic group $$G$$ of order $$16$$. A generator is $$x$$. I wish to find all the elements in $$G$$ of order $$8$$. I know how to find the generators and subgroups but I'm not sure how to find the elements, especially given that neither $$8$$ or $$16$$ are prime numbers..

If $$k\in\mathbb N$$, then the order of $$x^k$$ is equal to $$\frac{16}{\gcd(16,k)}$$. So, the elements of order $$8$$ are those $$x^k$$ such that $$\gcd(16,k)=2$$.