Show that every positive integer is a sum of one or more numbers of the form 2^r*3^s, where r and s are nonnegative integers and no summand divides another.

Remarks: This problem was originally created by Paul Erdős.
Note that the representations need not be unique: for instance, 11 = 2+9 = 3+8:

Of course to be much of a problem the addends must also be unique otherwise you could just use 1+1+1+1+...

Couldn't s be zero and just add in binary?
11 = 8+2+1
12 = 8+4
13 = 8+4+1
etc.

Never mind the above they violate: no summand divides another.
As I noticed just before I posted but decided to share anyway.

Posted by Jer on 2016-02-08 15:42:16