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3D vector product preserving length

Genady
in Linear Algebra and Group Theory

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I think that 28 is such a number. Do you agree?
I also think that it is the smallest such number. Do you agree with this?

Edited by Genady

4 hours ago, Genady said:

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I think that 28 is such a number. Do you agree?
I also think that it is the smallest such number. Do you agree with this?

Not quite sure about this since surely every number in N can be wriiten as the sum of 3 squares in R.

For instance 14 = (3)2 + (√3.5)2 + (√1.5)2

and 28 = 14*2

  • Author
2 minutes ago, studiot said:

Not quite sure about this since surely every number in N can be wriiten as the sum of 3 squares in R.

For instance 14 = (3)2 + (√3.5)2 + (√1.5)2

and 28 = 14*2

Right, but they specifically ask to show it in Z.

45 minutes ago, Genady said:

Right, but they specifically ask to show it in Z.

Z are the integers, not the natural numbers, N.

"Find a natural number..."

  • Author
1 minute ago, studiot said:

Z are the integers, not the natural numbers, N.

"Find a natural number..."

"Show that such a formula for three squares is impossible as an identity in the polynomial ring in 6 variables over Z."

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