Note "ls -Flc" appears to give ctime, not "modification time" mtime. It's actual usage varies greatly depending on your OS and is generally when the file's *status* changes, not the file data itself. See perldoc -f stat and especially "perldoc perlport" and then look for 'ctime' in the stat entry. Generally, atime >= mtime since it is the last access time or the modification time, whichever is more recent.

FWIW, depending on what you are trying to do, it may be impossible to guarantee that mtime/atime/ctime will be usefull. For example if users can touch files with arbitrary dates (e.g. using touch or "tar -xf" to dearchive a tree), then you have no real way of determining age based on atime or mtime (and perhaps ctime).