New answers tagged sums-of-squares
1
vote
Accepted
Express Two way ANOVA with interaction as matrix form
We have
$$y_{ijk}-\overline y=(\overline y_{i\cdot\cdot}-\overline y)+(\overline y_{\cdot j\cdot}-\overline y)+(\overline y_{ij\cdot}-\overline y_{i\cdot\cdot}-\overline y_{\cdot j\cdot}+\overline y)+(...
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5
votes
Accepted
For a number field $K$, is an integer a sum of two $K$'s elements squares iff it is a sum of two integer squares?
This is not true. For example, let $K=\Bbb{Q}(i)$ with
$\mathcal{O}_K=\Bbb Z[i]$. Then
$$
i = \left(\frac{1+i}{2}\right)^2 + \left(\frac{1+i}{2}\right)^2.
$$
This shows $i$ is a sum of two squares in $...
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