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:

(In reply to Solution by Brian Smith)

Very nicely done.  Yes, that is simpler than it seems.  Very elegant.

Posted by Steve Herman on 2016-02-29 11:31:50