If and can be written as the sum of 8 squares , then their product is also the sum of 8 squares . that means Show that the relationship between is :
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Originally Posted by simplependulum If and can be written as the sum of 8 squares , then their product is also the sum of 8 squares . that means Show that the relationship between is : it's straightforward if you're familiar with the normed division algebra of octonions. your question then is equivalent to proving that for any
This problem is related to the Degen's eight-square identity. Degen's eight-square identity - Wikipedia, the free encyclopedia
Last edited by mr fantastic; September 18th 2009 at 08:20 AM. Reason: Restored original reply
You can also do this with 16 and 32 squares by generalizing the octions. Not sure about 64 and beyond.
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