General basis representation problem
Looks like everything is back up to speed. Here’s a problem to celebrate:
Let
be a real number such that
and
be a finite collection of real numbers. Show that either there is a number such that
cannot be written as
where
is a positive integer and
, or there is a number which has multiple representations of this form.
Possibly relevant posts:
- Painting houses (1/21/2005)
- The sequence of all finite sequences (7/18/2005)
- Problem solving for non-geniuses (12/18/2004)