I'm reviewing for the math GRE (it's been 8+ years since I took abstract algebra) and came across this question:
A cyclic group of order 15 has an element $x$ such that the set $\{x^3, x^5, x^9 \}$ has exactly two elements. The number of elements in the set $\{x^{13n}: n \text{ a positive integer } \}$ is what?
Can someone show me how to approach this problem, and what concepts are in play here?