Mold/Mildew on Bathroom Ceiling

[Boater]

The bathroom of my cottage has a mold/mildew problem on the ceiling. I've cleaned it up several times in the last few years but it keeps coming back.

This season I'm going to install an exhaust fan and paint the ceiling.

Questions: Can I just clean up the ceiling again and paint it over? Will the mold find its way through again? Is there a special paint or technique I should use?

I'd appreciate advice from anyone who has dealt with this kind of problem.

Thanks.