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I have given a fraction in the form of $p/q$ , i want to express the given fraction as sum of series which is in the form of $1/x$ and $x$ is odd. i.e

$$ p/q = 1/x + 1/y+ 1/z+1/l/s $$ such that denominator is an odd number.

One trival way is to express $p/q = 1/q+1/q+1/q+....$($p$ times ). but i want length of the series to less than $p$.

How to do that ?

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    $\begingroup$ Greedy Egyptian algorithm might do. $\endgroup$ – Ivan Neretin Mar 27 '17 at 10:31
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    $\begingroup$ Possible duplicate of Prove that any rational can be expressed in the form $\sum\limits_{k=1}^n{\frac{1}{a_k}}$, $a_k\in\mathbb N^*$ $\endgroup$ – mvw Mar 27 '17 at 10:49
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    $\begingroup$ Not a duplicate exactly, as in this post denominators required to be odd. $\endgroup$ – coffeemath Mar 27 '17 at 11:23
  • $\begingroup$ Can't be less terms than $p$ if $p=1$. $\endgroup$ – Martin Rattigan Mar 27 '17 at 12:22
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    $\begingroup$ For some fractions $p/q$ it can be done with less than $p$ terms, but based on some empirical tests, whenever it can be done with less than $p$ terms, a greedy odd algorithm will find such a representation with the least number of terms. $\endgroup$ – quasi Mar 27 '17 at 12:41

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