Difference between revisions of "Euler's Four-Square Identity"
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''The product of the sum of the four squares is itself, the sum of four squares.'' | ''The product of the sum of the four squares is itself, the sum of four squares.'' | ||
| − | Mathematically, for any eight [[Complex numbers|complex numbers]] <math>x_1,x_2, x_3, x_4, y_1, y_2, y_3, y_4</math>, we must have <cmath> | + | Mathematically, for any eight [[Complex numbers|complex numbers]] <math>x_1,x_2, x_3, x_4, y_1, y_2, y_3, y_4</math>, we must have <cmath>asdfasaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa</cmath> |
Revision as of 11:30, 11 August 2018
Identity
The product of the sum of the four squares is itself, the sum of four squares.
Mathematically, for any eight complex numbers 
, we must have ![\[asdfasaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa\]](http://latex.artofproblemsolving.com/e/5/f/e5fe83583af74320ebf6a8a8cf895fe7e8ccd67b.png)
