Kudentoštkümnen nellikon identižuz

Pfisteran kudentoštkümnen nellikon identižuz om matematine teorem.

Kudentoštkümnen nellikon summoiden liža (произведение) om kudentoštkümnen nellikon summ.

Toziolendas:

$\,^{z_{1}=x_{1}y_{1}-x_{2}y_{2}-x_{3}y_{3}-x_{4}y_{4}-x_{5}y_{5}-x_{6}y_{6}-x_{7}y_{7}-x_{8}y_{8}+u_{1}y_{9}-u_{2}y_{10}-u_{3}y_{11}-u_{4}y_{12}-u_{5}y_{13}-u_{6}y_{14}-u_{7}y_{15}-u_{8}y_{16}}$

$\,^{z_{2}=x_{2}y_{1}+x_{1}y_{2}+x_{4}y_{3}-x_{3}y_{4}+x_{6}y_{5}-x_{5}y_{6}-x_{8}y_{7}+x_{7}y_{8}+u_{2}y_{9}+u_{1}y_{10}+u_{4}y_{11}-u_{3}y_{12}+u_{6}y_{13}-u_{5}y_{14}-u_{8}y_{15}+u_{7}y_{16}}$

$\,^{z_{3}=x_{3}y_{1}-x_{4}y_{2}+x_{1}y_{3}+x_{2}y_{4}+x_{7}y_{5}+x_{8}y_{6}-x_{5}y_{7}-x_{6}y_{8}+u_{3}y_{9}-u_{4}y_{10}+u_{1}y_{11}+u_{2}y_{12}+u_{7}y_{13}+u_{8}y_{14}-u_{5}y_{15}-u_{6}y_{16}}$

$\,^{z_{4}=x_{4}y_{1}+x_{3}y_{2}-x_{2}y_{3}+x_{1}y_{4}+x_{8}y_{5}-x_{7}y_{6}+x_{6}y_{7}-x_{5}y_{8}+u_{4}y_{9}+u_{3}y_{10}-u_{2}y_{11}+u_{1}y_{12}+u_{8}y_{13}-u_{7}y_{14}+u_{6}y_{15}-u_{5}y_{16}}$

$\,^{z_{5}=x_{5}y_{1}-x_{6}y_{2}-x_{7}y_{3}-x_{8}y_{4}+x_{1}y_{5}+x_{2}y_{6}+x_{3}y_{7}+x_{4}y_{8}+u_{5}y_{9}-u_{6}y_{10}-u_{7}y_{11}-u_{8}y_{12}+u_{1}y_{13}+u_{2}y_{14}+u_{3}y_{15}+u_{4}y_{16}}$

$\,^{z_{6}=x_{6}y_{1}+x_{5}y_{2}-x_{8}y_{3}+x_{7}y_{4}-x_{2}y_{5}+x_{1}y_{6}-x_{4}y_{7}+x_{3}y_{8}+u_{6}y_{9}+u_{5}y_{10}-u_{8}y_{11}+u_{7}y_{12}-u_{2}y_{13}+u_{1}y_{14}-u_{4}y_{15}+u_{3}y_{16}}$

$\,^{z_{7}=x_{7}y_{1}+x_{8}y_{2}+x_{5}y_{3}-x_{6}y_{4}-x_{3}y_{5}+x_{4}y_{6}+x_{1}y_{7}-x_{2}y_{8}+u_{7}y_{9}+u_{8}y_{10}+u_{5}y_{11}-u_{6}y_{12}-u_{3}y_{13}+u_{4}y_{14}+u_{1}y_{15}-u_{2}y_{16}}$

$\,^{z_{8}=x_{8}y_{1}-x_{7}y_{2}+x_{6}y_{3}+x_{5}y_{4}-x_{4}y_{5}-x_{3}y_{6}+x_{2}y_{7}+x_{1}y_{8}+u_{8}y_{9}-u_{7}y_{10}+u_{6}y_{11}+u_{5}y_{12}-u_{4}y_{13}-u_{3}y_{14}+u_{2}y_{15}+u_{1}y_{16}}$

$\,^{z_{9}=x_{9}y_{1}-x_{10}y_{2}-x_{11}y_{3}-x_{12}y_{4}-x_{13}y_{5}-x_{14}y_{6}-x_{15}y_{7}-x_{16}y_{8}+x_{1}y_{9}-x_{2}y_{10}-x_{3}y_{11}-x_{4}y_{12}-x_{5}y_{13}-x_{6}y_{14}-x_{7}y_{15}-x_{8}y_{16}}$

$\,^{z_{10}=x_{10}y_{1}+x_{9}y_{2}+x_{12}y_{3}-x_{11}y_{4}+x_{14}y_{5}-x_{13}y_{6}-x_{16}y_{7}+x_{15}y_{8}+x_{2}y_{9}+x_{1}y_{10}+x_{4}y_{11}-x_{3}y_{12}+x_{6}y_{13}-x_{5}y_{14}-x_{8}y_{15}+x_{7}y_{16}}$

$\,^{z_{11}=x_{11}y_{1}-x_{12}y_{2}+x_{9}y_{3}+x_{10}y_{4}+x_{15}y_{5}+x_{16}y_{6}-x_{13}y_{7}-x_{14}y_{8}+x_{3}y_{9}-x_{4}y_{10}+x_{1}y_{11}+x_{2}y_{12}+x_{7}y_{13}+x_{8}y_{14}-x_{5}y_{15}-x_{6}y_{16}}$

$\,^{z_{12}=x_{12}y_{1}+x_{11}y_{2}-x_{10}y_{3}+x_{9}y_{4}+x_{16}y_{5}-x_{15}y_{6}+x_{14}y_{7}-x_{13}y_{8}+x_{4}y_{9}+x_{3}y_{10}-x_{2}y_{11}+x_{1}y_{12}+x_{8}y_{13}-x_{7}y_{14}+x_{6}y_{15}-x_{5}y_{16}}$

$\,^{z_{13}=x_{13}y_{1}-x_{14}y_{2}-x_{15}y_{3}-x_{16}y_{4}+x_{9}y_{5}+x_{10}y_{6}+x_{11}y_{7}+x_{12}y_{8}+x_{5}y_{9}-x_{6}y_{10}-x_{7}y_{11}-x_{8}y_{12}+x_{1}y_{13}+x_{2}y_{14}+x_{3}y_{15}+x_{4}y_{16}}$

$\,^{z_{14}=x_{14}y_{1}+x_{13}y_{2}-x_{16}y_{3}+x_{15}y_{4}-x_{10}y_{5}+x_{9}y_{6}-x_{12}y_{7}+x_{11}y_{8}+x_{6}y_{9}+x_{5}y_{10}-x_{8}y_{11}+x_{7}y_{12}-x_{2}y_{13}+x_{1}y_{14}-x_{4}y_{15}+x_{3}y_{16}}$

$\,^{z_{15}=x_{15}y_{1}+x_{16}y_{2}+x_{13}y_{3}-x_{14}y_{4}-x_{11}y_{5}+x_{12}y_{6}+x_{9}y_{7}-x_{10}y_{8}+x_{7}y_{9}+x_{8}y_{10}+x_{5}y_{11}-x_{6}y_{12}-x_{3}y_{13}+x_{4}y_{14}+x_{1}y_{15}-x_{2}y_{16}}$

$\,^{z_{16}=x_{16}y_{1}-x_{15}y_{2}+x_{14}y_{3}+x_{13}y_{4}-x_{12}y_{5}-x_{11}y_{6}+x_{10}y_{7}+x_{9}y_{8}+x_{8}y_{9}-x_{7}y_{10}+x_{6}y_{11}+x_{5}y_{12}-x_{4}y_{13}-x_{3}y_{14}+x_{2}y_{15}+x_{1}y_{16}}$

kus

$u_{1}={\tfrac {(ax_{1}^{2}+x_{2}^{2}+x_{3}^{2}+x_{4}^{2}+x_{5}^{2}+x_{6}^{2}+x_{7}^{2}+x_{8}^{2})x_{9}-2x_{1}(bx_{1}x_{9}+x_{2}x_{10}+x_{3}x_{11}+x_{4}x_{12}+x_{5}x_{13}+x_{6}x_{14}+x_{7}x_{15}+x_{8}x_{16})}{c}}$

$u_{2}={\tfrac {(x_{1}^{2}+ax_{2}^{2}+x_{3}^{2}+x_{4}^{2}+x_{5}^{2}+x_{6}^{2}+x_{7}^{2}+x_{8}^{2})x_{10}-2x_{2}(x_{1}x_{9}+bx_{2}x_{10}+x_{3}x_{11}+x_{4}x_{12}+x_{5}x_{13}+x_{6}x_{14}+x_{7}x_{15}+x_{8}x_{16})}{c}}$

$u_{3}={\tfrac {(x_{1}^{2}+x_{2}^{2}+ax_{3}^{2}+x_{4}^{2}+x_{5}^{2}+x_{6}^{2}+x_{7}^{2}+x_{8}^{2})x_{11}-2x_{3}(x_{1}x_{9}+x_{2}x_{10}+bx_{3}x_{11}+x_{4}x_{12}+x_{5}x_{13}+x_{6}x_{14}+x_{7}x_{15}+x_{8}x_{16})}{c}}$

$u_{4}={\tfrac {(x_{1}^{2}+x_{2}^{2}+x_{3}^{2}+ax_{4}^{2}+x_{5}^{2}+x_{6}^{2}+x_{7}^{2}+x_{8}^{2})x_{12}-2x_{4}(x_{1}x_{9}+x_{2}x_{10}+x_{3}x_{11}+bx_{4}x_{12}+x_{5}x_{13}+x_{6}x_{14}+x_{7}x_{15}+x_{8}x_{16})}{c}}$

$u_{5}={\tfrac {(x_{1}^{2}+x_{2}^{2}+x_{3}^{2}+x_{4}^{2}+ax_{5}^{2}+x_{6}^{2}+x_{7}^{2}+x_{8}^{2})x_{13}-2x_{5}(x_{1}x_{9}+x_{2}x_{10}+x_{3}x_{11}+x_{4}x_{12}+bx_{5}x_{13}+x_{6}x_{14}+x_{7}x_{15}+x_{8}x_{16})}{c}}$

$u_{6}={\tfrac {(x_{1}^{2}+x_{2}^{2}+x_{3}^{2}+x_{4}^{2}+x_{5}^{2}+ax_{6}^{2}+x_{7}^{2}+x_{8}^{2})x_{14}-2x_{6}(x_{1}x_{9}+x_{2}x_{10}+x_{3}x_{11}+x_{4}x_{12}+x_{5}x_{13}+bx_{6}x_{14}+x_{7}x_{15}+x_{8}x_{16})}{c}}$

$u_{7}={\tfrac {(x_{1}^{2}+x_{2}^{2}+x_{3}^{2}+x_{4}^{2}+x_{5}^{2}+x_{6}^{2}+ax_{7}^{2}+x_{8}^{2})x_{15}-2x_{7}(x_{1}x_{9}+x_{2}x_{10}+x_{3}x_{11}+x_{4}x_{12}+x_{5}x_{13}+x_{6}x_{14}+bx_{7}x_{15}+x_{8}x_{16})}{c}}$

$u_{8}={\tfrac {(x_{1}^{2}+x_{2}^{2}+x_{3}^{2}+x_{4}^{2}+x_{5}^{2}+x_{6}^{2}+x_{7}^{2}+ax_{8}^{2})x_{16}-2x_{8}(x_{1}x_{9}+x_{2}x_{10}+x_{3}x_{11}+x_{4}x_{12}+x_{5}x_{13}+x_{6}x_{14}+x_{7}x_{15}+bx_{8}x_{16})}{c}}$

da

$a=-1,\;\;b=0,\;\;c=x_{1}^{2}+x_{2}^{2}+x_{3}^{2}+x_{4}^{2}+x_{5}^{2}+x_{6}^{2}+x_{7}^{2}+x_{8}^{2}\,.$

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