Timeline for Is -1 a sum of 2 squares in a certain field K?
Current License: CC BY-SA 2.5
6 events
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| Jun 22, 2010 at 14:21 | history | edited | Pete L. Clark | CC BY-SA 2.5 |
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| May 6, 2010 at 9:54 | comment | added | Keivan Karai | The special case Kevin mentioned has a short proof which makes it easy to remember: if $-1=a^2+b^2+c^2$ then $-1-c^2=a^2+b^2$ implying $-1=(a^2+b^2)(1+c^2)/(1+c^2)^2$. Now use the fact that the product of the sum of two squares is also a sum of two squares. | |
| May 6, 2010 at 6:07 | vote | accept | Mikhail Borovoi | ||
| May 5, 2010 at 21:52 | history | edited | Pete L. Clark | CC BY-SA 2.5 |
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| May 5, 2010 at 19:36 | comment | added | Kevin Buzzard | My favourite "well known to quadratic forms specialists" fact---I hope I've remembered it right---if K is a field and -1 is the sum of three squares in K then it's the sum of two squares in K. | |
| May 5, 2010 at 18:35 | history | answered | Pete L. Clark | CC BY-SA 2.5 |