The question is as follow: Show that if a circle homeomorphism has a periodic point of minimal period $k\geq 1$, then it cannot have any periodic points of any other periods.
One thing I tried is, I suppose there is periodic points of other minimal periods, say there is $y$ such that $f^l(y) = y$ and I was thinking to use the fact that homeomorphism is strictly monotone, i.e either $x<y$ or $y>x$, then I want to try to reach contradiction, but I do not know how to proceed. Is there any hint?
