## Recovering a set of discrete values [closed]

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I have a set of positive integers $a$, where $\displaystyle\sum_i{a_i}=700$ and $\displaystyle\sum_i{a_i^2}=1212$.

Is there a unique decomposition of $a$ and, if so, how do I recover it?

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I'm afraid your question is not appropriate for MathOverflow (please see the FAQ). You are likely to get help if you ask the nice people at math.stackexchange.com  Before you do so, you might want to ask yourself just how strong a constraint two equations will put on a potentially large number of variables. – S. Carnahan♦ Apr 12 2011 at 19:40
Also, there is no set of positive integers that will work.  A multiset might.  Gerhard "Ask Me About System Design" Paseman, 2010.04.12 – Gerhard Paseman Apr 12 2011 at 20:44
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