TITLE: Concerning: presentations of rational numbers into sums
QUESTION [5 upvotes]: Problem: Prove that all positive rational numbers can be expressed as the finite sum of different numbers $\displaystyle \frac {1} {n}$ ($n$ is a natural number).
Example: $\displaystyle \frac {19}{16}=1+ \frac {1}{8} + \frac {1}{16}.$
*We cant sum numbers as $\displaystyle \frac {3}{16}$ (denominator > 1) but we can sum $\displaystyle \frac {1}{8}+ \frac {1}{16}.$
Any solutions? Suggestions?

REPLY [6 votes]: This is a putnam problem. For a complete solution please look here.

Take a look at this article as well: J.C.Owings, American Mathematical Monthly Vol. 75 (1968), Pages $777-778$.