81 chars: 
$ perl -e '($n,$d)=split"/",pop;{1while++$x<$d/$n;warn"1/$x\n";$n=$n*$
+x-$d;$d*=$x;redo if$n}' 18/20
1/2
1/3
1/15

[download]
Update: changing the entire structure to a C-style for-loop saves 2 chars, so this gives me a 79-char solution: 
for(($n,$d)=split"/",pop;$n;){1while++$x<$d/$n;warn"1/$x\n";$n=$n*$x-$
+d;$d*=$x}

[download]
<Reveal this spoiler or all in this thread>

blokhead

In reply to Re^2: Egyptian fractions (Golf Anyone?) by blokhead
in thread Egyptian fractions by jimt

Title:
Use:  <p> text here (a paragraph) </p>
and:  <code> code here </code>
to format your post, it's "PerlMonks-approved HTML":


  • Posts are HTML formatted. Put <p> </p> tags around your paragraphs. Put <code> </code> tags around your code and data!
  • Titles consisting of a single word are discouraged, and in most cases are disallowed outright.
  • Read Where should I post X? if you're not absolutely sure you're posting in the right place.
  • Please read these before you post! —
  • Posts may use any of the Perl Monks Approved HTML tags:
    a, abbr, b, big, blockquote, br, caption, center, col, colgroup, dd, del, details, div, dl, dt, em, font, h1, h2, h3, h4, h5, h6, hr, i, ins, li, ol, p, pre, readmore, small, span, spoiler, strike, strong, sub, summary, sup, table, tbody, td, tfoot, th, thead, tr, tt, u, ul, wbr
  • You may need to use entities for some characters, as follows. (Exception: Within code tags, you can put the characters literally.)
            For:     Use:
    & &amp;
    < &lt;
    > &gt;
    [ &#91;
    ] &#93;
  • Link using PerlMonks shortcuts! What shortcuts can I use for linking?
  • See Writeup Formatting Tips and other pages linked from there for more info.