Consider the following system of equations:


$$
\sum\_{i=1}^{2n}a\_i=0 
$$
$$
\sum\_{i=1}^{2n}\frac{1}{a\_i}=0
$$
Where for each $i$ $a\_i$ is an odd integer and the $a\_i$ are not necessarly distinct. A solution $(a\_1,\dots,a\_{2n})$ is trivial
if (after some permutation of the coefficients) for each $i$ we have 
$$a\_i=-a\_{n+i}$$.
I know that if $n>2$ there exist non trivial solutions. My questions are:


* What is the minimum number of variables for which there exist non trivial solutions ?
* Can you exhibit a minimal solution or at least a solution you think could be minimal ?



A Diophantine problem related to egyptian fractions
Well, -1,3,3,5,5,-15 comes to mind. This is 2n variables for n=3. But you said you know there are non-trivial solutions for n>2. Did you mean "for every n>2" ? If so, what are you asking? Also, why not consider the case of an odd number of integers (some of which would be even)?


