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The original problem states $\sum_{i=1}^k n_i = n$. However, I'm having trouble trying to figure out how to simplify this: $\sum_{i=1}^k n_i^2$.

I've been trying it and I don't think I can just simply write $n^2$, so can anyone point me in the right direction?

Thanks!

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    $\begingroup$ There is no relation bewteen the sum of numbers and the sum of their squares, except for the trivial case $k=1$. $\endgroup$
    – user65203
    Sep 5 '16 at 15:08
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Without knowing something about the $n_i$ you can't do anything. Compare $k=2$ with $(n_1,n_2)= (3,3)$ and $(1,5)$

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