Timeline for sums of rational squares
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 16, 2012 at 7:36 | comment | added | François Brunault | The fact that $p \equiv 3 \pmod{4}$ can't be written as a sum of two rational squares can also be proved $p$-adically : if $p d^2 = a^2+b^2$ then $-1$ would be a square mod $p$, which is impossible. In modern language the equation $p=x^2+y^2$ has obstruction precisely at $2$ and at $p$. | |
| Feb 15, 2012 at 22:05 | vote | accept | Michael Beeson | ||
| Feb 15, 2012 at 20:23 | comment | added | Cam McLeman | Ah, the ol' "clearing the denominator trick." Great! | |
| Feb 15, 2012 at 20:19 | comment | added | Will Sawin | Can't one just say that if a=(b/c)^2+(d/e)^2, then ac^2e^2=(be)^2+(cd)^2? So this reduces to the statement that if a number can't be written as the sum of two integer squares, then that number times a square can't be written as the sum of two integer squares. But this is obvious given the theorem on which numbers are the sum of two integer squares. | |
| Feb 15, 2012 at 20:01 | history | answered | Cam McLeman | CC BY-SA 3.0 |